second order approximation of the pseudoinverse for operator deconvolutions and families of ill posed problems we identify a more accurate means of deconvolving compact nondegenerate operators than that provided by independent application of standard regularization techniques to individual members of the implied continuum of first kind integral equations for the problem defined by h x t int y f x y g y t dy where it is required to find g y t given noise corrupted versions of square integrable f x y and h x t it is shown that greater accuracy results from optimizing solutions for each member of the sequence of integral equations derived from individual components of the singular value expansion of h x t than from optimizing solutions to each of the equations determined by different fixed values of t this result has particular implications for treatment of the bioelectric biomagnetic source imaging problems where the characteristic need to perform such a deconvolution has been previously handled by producing an individually regularized solution to the above equation for each t in a collection of

superior properties of the presb preconditioner for operators on two by two block form with square blocks matrices or operators in two by two block form with square blocks arise in numerous important applications such as in optimal control problems for pdes the problems are normally of very large scale so iterative solution methods must be used thereby the choice of an efficient and robust preconditioner is of crucial importance since some time a very efficient preconditioner the preconditioned square block presb method has been used by the authors and coauthors in various applications in particular for optimal control problems for pdes it has been shown to have excellent properties such as a very fast and robust rate of convergence that outperforms other methods in this paper the fundamental and most important properties of the method are stressed and presented with new and extended proofs under certain conditions the condition number of the preconditioned matrix is bounded by 2 or even smaller furthermore under certain assumptions the rate of convergence is superlinear

inverse problem in avalanche dynamics models 1 avalanche dynamics models are increasingly used to estimate the features of extremely rare events for avalanche zoning they employ a frictional coefficient which reflects something close to snow viscosity as this coefficient is more conceptual than physical it cannot be measured and must be fitted by matching avalanche dynamics model results and field data however most of the time the historical record is not long enough to fit this coefficient for extremely rare events here we propose a deterministic inversion method to obtain the probability density function of this coefficient the method has been applied to two avalanche paths in the french alps each with a sustained avalanche activity over the last century for applications the voellmy avalanche dynamics model has been used with no loss of generality it is shown that the friction coefficient is a random variable whose marginal probability distribution varies rapidly and exhibits two or more peaks

large scale tikhonov regularization via reduction by orthogonal projection abstract this paper presents a new approach to computing an approximate solution of tikhonov regularized large scale ill posed least squares problems with a general regularization matrix the iterative method applies a sequence of projections onto generalized krylov subspaces a suitable value of the regularization parameter is determined by the discrepancy principle

the design of trellis coded mpsk for fading channels set partitioning for optimum code design a previous work on criteria for designing trellis coded mpsk modulation to achieve minimum error probability performance on the rician fading channel see ibid vol 36 no 9 p 1004 1012 sep 1988 is extended it is demonstrated that allowing for multiple symbols per trellis branch i e multiple trellis coded modulation mtcm provides an additional degree of freedom for designing a code to meet the optimization on the fading channel diversities larger than those achievable with conventional trellis codes having the same number of trellis states are now attainable it is under these conditions that mtcm achieves its full potential

a regularizing lanczos iteration method for underdetermined linear systems this paper is concerned with the solution of underdetermined linear systems of equations with a very ill conditioned matrix a whose dimensions are so large to make solution by direct methods impractical or infeasible image reconstruction from projections often gives rise to such systems in order to facilitate the computation of a meaningful approximate solution we regularize the linear system i e we replace it by a nearby system that is better conditioned the amount of regularization is determined by a regularization parameter its optimal value is in most applications not known a priori we present a new iterative method based on the lanczos algorithm for determining a suitable value of the regularization parameter by the discrepancy principle and an approximate solution of the regularized system of equations

chernoff bound of trellis coded modulation over correlated fading channels we derive a chernoff upper bound for the pairwise error probability in the presence of an additive white gaussian noise and a rayleigh or rice correlated fading the bound is useful for situations where perfect interleaving cannot be achieved we use it to determine some indications in the design of optimum trellis coded modulation for correlated fading channels

stability estimates and structural spectral properties of saddle point problems for a general class of saddle point problems sharp estimates for babuska s inf sup stability constants are derived in terms of the constants in brezzi s theory in the finite dimensional hermitian case more detailed spectral properties of preconditioned saddle point matrices are presented which are helpful for the convergence analysis of common krylov subspace methods the theoretical results are applied to two model problems from optimal control with time periodic state equations numerical experiments with the preconditioned minimal residual method are reported

space time codes for high data rate wireless communication performance criteria in the presence of channel estimation errors mobility and multiple paths space time coding is a bandwidth and power efficient method of communication over fading channels that realizes the benefits of multiple transmit antennas specific codes have been constructed using design criteria derived for quasi static flat rayleigh or rician fading where channel state information is available at the receiver it is evident that the practicality of space time codes will be greatly enhanced if the derived design criteria remain valid in the absence of perfect channel state information it is even more desirable that the design criteria not be unduly sensitive to frequency selectivity and to the doppler spread this paper presents a theoretical study of these issues beginning with the effect of channel estimation error here it is assumed that a channel estimator extracts fade coefficients at the receiver and for constellations with constant energy it is proved that in the absence of ideal channel state information the design criteria for space time codes is still valid the analysis also demonstrates that standard channel estimation techniques can be used in conjunction with space time codes provided that the number of transmit antennas is small we also derive the maximum likelihood detection metric in the presence of channel estimation errors next the effect of multiple paths on the performance of space time codes is studied for a slowly changing rayleigh channel it is proved that the presence of multiple paths does not decrease the diversity order guaranteed by the design criteria used to construct the space time codes similar results hold for rapid fading channels with or without multiple paths the conclusion is that the diversity order promised by space time coding is achieved under a variety of mobility conditions and environmental effects

model adaptivity for goal oriented inference using adjoints abstract an inverse problem seeks to infer unknown model parameters using observed data we consider a goal oriented inverse problem where the goal of inferring parameters is to use them in predicting a quantity of interest qoi recognizing that multiple models of varying fidelity and computational cost may be available to describe the physical system we formulate a goal oriented model adaptivity approach that leverages multiple models while controlling the error in the qoi prediction in particular we adaptively form a mixed fidelity model by using models of different levels of fidelity in different subregions of the domain taking the solution of the inverse problem with the highest fidelity model as our reference qoi prediction we derive an adjoint based third order estimate for the qoi error from using a lower fidelity model localization of this error then guides the formation of mixed fidelity models we demonstrate the method for example problems described by convection diffusion reaction models for these examples our mixed fidelity models use the high fidelity model over only a small portion of the domain but result in qoi estimates with small relative errors we also demonstrate that the mixed fidelity inverse problems can be cheaper to solve and less sensitive to the initial guess than the high fidelity inverse problems

tikhonov regularization and the l curve for large discrete ill posed problems discretization of linear inverse problems generally gives rise to very ill conditioned linear systems of algebraic equations typically the linear systems obtained have to be regularized to make the computation of a meaningful approximate solution possible tikhonov regularization is one of the most popular regularization methods a regularization parameter specifies the amount of regularization and in general an appropriate value of this parameter is not known a priori we review available iterative methods and present new ones for the determination of a suitable value of the regularization parameter by the l curve criterion and the solution of regularized systems of algebraic equations

set partitioning for multilevel codes on a rayleigh fading channel on a rayleigh fading channel multilevel codes achieve larger hamming distances than single level codes at comparable decoder complexity and bandwidth efficiency by employing a multistage decoder typically multilevel codes are designed using ungerboeck s 1982 set partitioning this results in a large path multiplicity that degrades the code performance significantly in order to overcome the performance degradation we propose a set partitioning method that greatly reduces the path multiplicity

construction of new mpsk trellis codes for fading channels in this paper a new methodology for design of mpsk trellis codes on fading channels is proposed the proposed design criteria based on effective code length the minimum product distance and the minimum euclidean distance are used to construct new 8 psk and 16 psk trellis codes with improved bit error rate performance on fading channels the code performance is evaluated analytically and by monte carlo simulation the results show that the proposed codes achieve significant improvements relative to the best known codes

convergence analysis of lsqr for compact operator equations abstract in this paper we analyze the behavior of the lsqr algorithm for the solution of compact operator equations in hilbert spaces we present results concerning existence of krylov solutions and the rate of convergence in terms of an l p sequence where p depends on the summability of the singular values of the operator under stronger regularity requirements we also consider the decay of the error finally we study the approximation of the dominant singular values of the operator attainable with the bidiagonal matrices generated by the lanczos bidiagonalization and the arising low rank approximations some numerical experiments on classical test problems are presented

generalized arnoldi tikhonov method for sparse reconstruction this paper introduces two new algorithms belonging to the class of arnoldi tikhonov regularization methods which are particularly appropriate for sparse reconstruction the main idea is to consider suitable adaptively defined regularization matrices that allow the usual 2 norm regularization term to approximate a more general regularization term expressed in the p norm p geq 1 the regularization matrix can be updated both at each step and after some iterations have been performed leading to two different approaches the first one is based on the idea of the iteratively reweighted least squares method and can be obtained considering flexible krylov subspaces the second one is based on restarting the arnoldi algorithm numerical examples are given in order to show the effectiveness of these new methods and comparisons with some other already existing algorithms are made

a regularization parameter in discrete ill posed problems the tikhonov regularization method for discrete ill posed problems is considered for the practical choice of the regularization parameter alpha some authors use a plot of the norm of the regularized solution versus the norm of the residual vector for all alpha considered this paper contains an analysis of the shape of this plot and gives a theoretical justification for choosing the regularization parameter so it is related to the l corner of the plot considered in the logarithmic scale moreover a new criterion for choosing alpha is introduced independent of the shape of the plot which gives a new interpretation of the corner criterion mentioned above the existence of l corner is discussed

a novel approach for studies of multispectral bioluminescence tomography bioluminescence tomography blt is a promising new area in biomedical imaging the goal of blt is to provide quantitative reconstruction of bioluminescent source distribution within a small animal from optical signals on the animal s body surface the multispectral version of blt takes advantage of the measurement information in different spectrum bands in this paper we propose a novel approach for the multispectral blt the new feature of the mathematical framework is to use numerical prediction results based on two related but distinct boundary value problems this mathematical framework includes the conventional framework in the study of multispectral blt for the new framework introduced here we establish the solution existence uniqueness and continuous dependence on data and characterize the limiting behaviors when the regularization parameter approaches zero or when the penalty parameter approaches infinity we study two kinds of numerical schemes for multispectral blt and derive error estimates for the numerical solutions we also present numerical examples to show the performance of the numerical methods

analysis of the error performance of trellis coded modulations in rayleigh fading channels this work presents an exact expression for the pairwise error event probability of trellis coded modulation tcm transmitted over rayleigh fading channels it includes phase shift keying psk and multilevel quadrature amplitude modulation qam codes as well as coherent and partially coherent e g differential pilot tone etc detection due to the form of the exact pairwise error event probabilities this calculation technique cannot be used with the transfer function technique to obtain an upper union bound on the overall bit error probability for this reason the authors estimate the bit error probability by considering only a small number of short error events through simulations they found that the estimation is usually very accurate at high signal to noise ratios but not as accurate at lower signal to noise ratios they study several coded modulation schemes this way among the results are the fact that tcm provides significant improvement in the error floor when detected differentially and an asymmetry in the pairwise error event probability for 16 qam

iterative regularization method in generalized inverse beamforming abstract beamforming based on microphone array is a method to identify sound sources it can visualize the sound field of the source plane and reveal interesting acoustic information generalized inverse beamforming gib is one important branch of beamforming techniques due to its high identification accuracy and computational efficiency however in real testing situation errors caused by measurement noise and configuration problems may seriously reduce the beamforming accuracy as an inverse problem the stability of gib can be improved with regularization methods we proposed a new iterative regularization method for gib by iteratively redefining the form of regularization matrix and calculating the corresponding solution moreover the new method is applied to functional beamforming and double layer antenna beamforming respectively numerical simulations and experiments are implemented the results show that the proposed regularization method leads to more robust beamforming output and higher accuracy in both the two applications

on the finite embeddability property for residuated ordered groupoids the finite embeddability property fep for integral commutative residuated ordered monoids was established by w j blok and c j van alten in 2002 using higman s finite basis theorem for divisibility orders we prove that the assumptions of commutativity and associativity are not required the classes of integral residuated ordered monoids and integral residuated ordered groupoids have the fep as well the same holds for their respective subclasses of bounded semi lattice ordered structures the assumption of integrality cannot be dropped in general the class of commutative residuated lattice ordered monoids does not have the fep but the class of n potent commutative residuated lattice ordered monoids does have the fep for any n

residuated frames with applications to decidability residuated frames provide relational semantics for substructural logics and are a natural generalization of kripke frames in intuitionistic and modal logic and of phase spaces in linear logic we explore the connection between gentzen systems and residuated frames and illustrate how frames provide a uniform treatment for semantic proofs of cut elimination the finite model property and the finite embeddability property we use our results to prove the decidability of the equational and or universal theory of several varieties of residuated lattice ordered groupoids including the variety of involutive

a stopping criterion for the conjugate gradient algorithm in a finite element method framework the conjugate gradient method has always been successfully used in solving the symmetric and positive definite systems obtained by the finite element approximation of self adjoint elliptic partial differential equations taking into account recent results 13 19 20 22 which make it possible to approximate the energy norm of the error during the conjugate gradient iterative process we adapt the stopping criterion introduced in 3 moreover we show that the use of efficient preconditioners does not require to change the energy norm used by the stopping criterion finally we present the results of several numerical tests that experimentally validate the effectiveness of our stopping criterion

a pseudo heuristic parameter selection rule for l1 regularized minimization problems abstract this paper considers the regularization parameter determination of l 1 regularized minimization problem we solve the l 1 regularized problem using iterative reweighted least squares irls which involves solving a linear system whose coefficient matrix has the form m 1 n 0 1 the aim of this paper is to find an efficient and computationally inexpensive algorithm to both choose the regularization parameter and solve the l 1 regularized problem in order to achieve this we propose an irls algorithm with adaptive regularization parameter selection based on a heuristic parameter determination rule de boor s parameter selection criterion compared with some of the state of the art algorithms and parameter selection rules the numerical experiments show the efficiency and robustness of the proposed method

mesh independent superlinear pcg rates via compact equivalent operators the subject of the paper is the mesh independent convergence of the preconditioned conjugate gradient pcg method for nonsymmetric elliptic problems the approach of equivalent operators is involved in which one uses the discretization of another suitable elliptic operator as preconditioning matrix by introducing the notion of compact equivalent operators it is proved that for a wide class of elliptic problems the superlinear convergence of the obtained pcg method is mesh independent under finite element discretizations that is the rate of superlinear convergence is given in the form of a sequence which is mesh independent and is determined only by the elliptic operators

multilevel trellis coded modulations for the rayleigh fading channel the authors present coded 8 phase shift keyed 8 psk modulations for the rayleigh fading channel the schemes are based on multilevel trellis coded modulation constructions and utilize maximum free hamming distance binary convolutional codes as building blocks a suboptimal multistage decoder that utilizes interstage interleaving and iterative decoding is proposed and evaluated examples are constructed to show that the proposed schemes outperform the best modified codes of the ungerboeck type due to significantly higher implicit time diversity yielding seven branches of built in time diversity whereas the ungerboeck code yields four branches of time diversity for a 64 state system the transmission delay is higher however the new schemes can provide three levels of unequal error protection when 8 psk or 8 differential phase shift keying 8 dpsk modulations are used they provide 10 14 db channel signal to noise ratio gain over uncoded 4 dpsk at a bit error rate of 10 sup 3 for a modest decoding complexity

some history of the conjugate gradient and lanczos methods this paper gives some of the history of the conjugate gradient and lanczos algorithms and an annotated bibliography for the period 1948 1976

some properties of the arnoldi based methods for linear ill posed problems in this paper we study some properties of the classical arnoldi based methods for solving infinite dimensional linear equations involving compact operators these problems are intrinsically ill posed since a compact operator does not admit a bounded inverse we study the convergence properties and the ability of these algorithms to estimate the dominant singular values of the operator

formal concept analysis and lattice valued chu systems this paper links formal concept analysis fca both to order theoretic developments in the theory of galois connections and to chu spaces or systems viewed as a common rubric for both topological systems and systems arising from predicate transformers in programming semantics 13 these links are constructed for each of traditional fca and l fca where l is a commutative residuated semiquantale surprising and important consequences include relationships between formal l contexts and l topological systems within the category of l chu systems relationships justifying the categorical study of formal l contexts and linking such study to l chu systems applications and potential applications are primary motivations including several example classes of formal l contexts induced from data mining notions throughout categorical frameworks are given for fca and lattice valued fca in which morphisms preserve the birkhoff operators on which all the structures of fca and lattice valued fca rest and further the results of this paper show that under very general conditions these categorical frameworks are both sufficient and necessary for the interchange or preservation of l concepts and l protoconcepts structures central to fca and lattice valued fca

superlinear convergence using block preconditioners for the real system formulation of complex helmholtz equations abstract complex valued helmholtz equations arise in various applications and a lot of research has been devoted to finding efficient preconditioners for the iterative solution of their discretizations in this paper we consider the helmholtz equation rewritten in real valued block form and use a preconditioner in a special two by two block form we show that the corresponding preconditioned krylov iteration converges at a mesh independent superlinear rate

reconstruction of distributed dynamic loads on an euler beam via mode selection and consistent spatial expression this paper presents a convenient and efficient approach to reconstruct two dimensional distributed dynamic loads on a damped thin elastic plate from its steady state dynamic response the approach is based on a mode selection method which comes from an idea that an optimal range of frequency and mode exists for dynamic load reconstruction as well as on the consistent spatial expression of the distributed dynamic loads the criterion for mode selection is derived theoretically a comparison between the method of truncated singular value decomposition tsvd and the method of mode selection demonstrates that the former is unstable while the latter is not only stable but robust with the proposed criterion the method of mode selection enables one to find an optimal range for load reconstruction provided that the error bounds of both parameters and objective are given or estimated and hence to make a balance between the reconstruction range and the error control

rational krylov and adi iteration for infinite size quasi toeplitz matrix equations abstract we consider a class of linear matrix equations involving semi infinite matrices which have a quasi toeplitz structure these equations arise in different settings mostly connected with pdes or the study of markov chains such as random walks on bidimensional lattices we present the theory justifying the existence of the solution in an appropriate banach algebra which is computationally treatable and we propose several methods for computing them we show how to adapt the adi iteration to this particular infinite dimensional setting and how to construct rational krylov methods convergence theory is discussed and numerical experiments validate the proposed approaches

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

some properties of range restricted gmres methods the gmres method is one of the most popular iterative schemes for the solution of large linear systems of equations with a square nonsingular matrix gmres type methods also have been applied to the solution of linear discrete ill posed problems computational experience indicates that for the latter problems variants of the standard gmres method that require the solution to live in the range of a positive power of the matrix of the linear system of equations to be solved generally yield more accurate approximations of the desired solution than standard gmres this paper investigates properties of these variants of gmres

adaptive trellis coded multiple phase shift keying for rayleigh fading channels an adaptive scheme for trellis coded modulation of mpsk signals called adaptive trellis coded multiple phaseshift keying atcmpsk is proposed for slowly rayleigh fading channels the adaptive scheme employs a slightly modified rate 1 2 convolutional encoder and the corresponding viterbi decoder to realize a family of codes of different rates which are employed according to channel conditions during poor channel conditions trellis coded qpsk tcqpsk together with repetition schemes are employed as channel conditions improve higher rate schemes such as trellis coded 16 psk are used an interleaving deinterleaving method suitable for the adaptive scheme is proposed theoretical bounds for the error performance and an exact expression for the throughput of the proposed adaptive scheme are derived and are compared against simulation results simulations have been performed to measure the performance of the scheme for different parameters and some nonideal conditions it is shown that atcmpsk results in considerable improvement in bit error rate ber performance of mpsk signals under ideal conditions gains in the range of 3 20 db are achieved over conventional fixed rate pragmatic trellis coded schemes

arnoldi tikhonov regularization methods tikhonov regularization for large scale linear ill posed problems is commonly implemented by determining a partial lanczos bidiagonalization of the matrix of the given system of equations this paper explores the possibility of instead computing a partial arnoldi decomposition of the given matrix computed examples illustrate that this approach may require fewer matrix vector product evaluations and therefore less arithmetic work moreover the proposed range restricted arnoldi tikhonov regularization method does not require the adjoint matrix and hence is convenient to use for problems for which the adjoint is difficult to evaluate

near capacity turbo trellis coded modulation design based on exit charts and union bounds transactions papers bandwidth efficient parallel concatenated turbo trellis coded modulation ttcm schemes were designed for communicating over uncorrelated rayleigh fading channels a symbol based union bound was derived for analysing the error floor of the proposed ttcm schemes a pair of in phase i and quadrature phase q interleavers were employed for interleaving the i and q components of the ttcm coded symbols in order to attain an increased diversity gain the decoding convergence of the iq ttcm schemes was analysed using symbol based extrinsic information transfer exit charts the best ttcm component codes were selected with the aid of both the symbolbased union bound and non binary exit charts for designing capacity approaching iq ttcm schemes in the context of 8 psk 16 qam 32 qam and 64 qam modulation schemes

bandwidth efficient concatenated coding schemes for fading channels concatenated codes consisting of trellis inner codes and reed solomon outer codes are considered to achieve large coding gains with small bandwidth expansion in the presence of frequency nonselective slow rician fading both errors only and errors erasures decoding algorithms for outer codes are applied new upper bounds on bit error probability performance in the presence of fading are obtained and compared with simulation results for zero channel memory the effect of interleaving in eliminating channel memory is investigated the performance gains that are achieved by the coding scheme relative to the reference uncoded systems are illustrated via some examples

rate 5 6 trellis coded 8 psk some new short constraint length codes are described for satellite channels which are constant envelope and which have spectral and energy efficiencies intermediate to other recent coded techniques namely r 2 3 coded 8 psk and r 3 4 coded 16 psk we use two intervals of 8 psk transmission to form a modulation base for r 5 6 trellis codes a particularly attractive design is an eight state code producing 6 2 db gain on the gaussian channel over uncoded 8 psk yet sacrificing only 16 percent in spectral efficiency

multiple trellis coded frequency and phase modulation multiple trellis coded modulation of constant envelope frequency and phase modulated signal sets mtcm fpm is investigated for performance on the additive white gaussian noise awgn channel and on the one sided normal rayleigh and rician fading channels the nakagami m fading model is used as an alternative to the rician fading model to calculate the error probability upper bound for trellis coded schemes on the fading channel the likeliness and the disparity between the upper bounds to the error probability for the two fading models are discussed the design criteria for the one sided normal fading channel modeled by the nakagami m distribution are observed to be the same as those for the rayleigh fading channel for the mtcm fpm schemes it is demonstrated that the set partitioning designed to maximize symbol diversity optimum for fading channels is optimum for performance on the awgn channel as well the mtcm fpm schemes demonstrate improved performance over mtcm mpsk schemes and tcm fpm schemes on the awgn channel and the fading channel

automatic parameter setting for arnoldi tikhonov methods in the framework of iterative regularization techniques for large scale linear ill posed problems this paper introduces a novel algorithm for the choice of the regularization parameter when performing the arnoldi tikhonov method assuming that we can apply the discrepancy principle this new strategy can work without restrictions on the choice of the regularization matrix moreover this method is also employed as a procedure to detect the noise level whenever it is just overestimated numerical experiments arising from the discretization of integral equations and image restoration are presented

fast linearized alternating direction minimization algorithm with adaptive parameter selection for multiplicative noise removal owing to the edge preserving ability and low computational cost of the total variation tv variational models with the tv regularizer have been widely investigated in the field of multiplicative noise removal the key points of the successful application of these models lie in the optimal selection of the regularization parameter which balances the data fidelity term with the tv regularizer the efficient algorithm to compute the solution in this paper we propose two fast algorithms based on the linearized technique which are able to estimate the regularization parameter and recover the image simultaneously in the iteration step of the proposed algorithms the regularization parameter is adjusted by a special discrepancy function defined for multiplicative noise the convergence properties of the proposed algorithms are proved under certain conditions and numerical experiments demonstrate that the proposed algorithms overall outperform some state of the art methods in the psnr values and computational time

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

simultaneous solution of large scale linear systems and eigenvalue problems with a parallel gmres method a method for simultaneous solution of large and sparse linearized equation sets and the corresponding eigenvalue problems is presented such problems arise from the discretization and the solution of nonlinear problems with the finite element method and newton iteration the method is based on a parallel version of the preconditioned gmres m by deflation the parallel code exploits the architecture of the computational clusters using the mpi message passing interface the convergence rate the parallel speedup and the memory requirements of the proposed method are reported and evaluated

on the computation of gauss quadrature rules for measures with a monomial denominator let d be a nonnegative measure with support on the real axis and let r be outside the convex hull of the support this paper describes a new approach to determining recursion coefficients for gauss quadrature rules associated with measures of the form d x d x x 2 the proposed method is based on determining recursion coefficients for a suitable family of orthonormal laurent polynomials numerical examples show this approach to yield higher accuracy than available methods

a modified design of trellis coded mpsk for the fading channel it is shown that the classical additive white gaussian noise awgn channel design can be retained for the fading channel with any degree of fading if carried out with the appropriate signal set size m m sub min the size of the signal set m sub min is shown to depend upon the number of parallel transitions between a given pair of states and the throughput rate in the proposed multiple trellis coded modulation mtcm scheme with a modified design mtcm md the output bits from a rate m m 1 trellis encoder are assigned multiple signals from an m sub min psk signal set compared to the mtcm with set partitioning proposed for the fading channel spf design the mtcm md scheme provides the same signal diversity and the same or increased values of the branch distance product and always leads to increased value of d sup 2 free as a result the performance is always improved on the rician fading channel due to the increased d sup 2 free and is improved on any fading channel when an increase in branch distance produce p takes place when compared to the mtcm with the set partitioning optimum for the awgn channel spa design the mtcm md scheme under certain conditions provides the same value of d sup 2 free as the mtcm spa design and is then asymptotically optimum for both the awgn channel and the fading channels

conditional gradient tikhonov method for a convex optimization problem in image restoration in this paper we consider the problem of image restoration with tikhonov regularization as a convex constrained minimization problem using a kronecker decomposition of the blurring matrix and the tikhonov regularization matrix we reduce the size of the image restoration problem therefore we apply the conditional gradient method combined with the tikhonov regularization technique and derive a new method we demonstrate the convergence of this method and perform some numerical examples to illustrate the effectiveness of the proposed method as compared to other existing methods

finite element approach to clustering of multidimensional time series we present a new approach to clustering of time series based on a minimization of the averaged clustering functional the proposed functional describes the mean distance between observation data and its representation in terms of mathbf k abstract models of a certain predefined class not necessarily given by some probability distribution for a fixed time series x t this functional depends on mathbf k sets of model parameters theta theta 1 dots theta mathbf k and mathbf k functions of cluster affiliations gamma gamma 1 t dots gamma mathbf k t characterizing the affiliation of any element x t of the analyzed time series to one of the mathbf k clusters defined by the considered model parameters we demonstrate that for a fixed set of model parameters theta the appropriate tykhonov type regularization of this functional with some regularization factor epsilon 2 results in a minimization problem similar to a variational problem usually associated with one dimensional nonhomogeneous partial differential equations this analogy allows us to apply the finite element framework to the problem of time series analysis and to propose a numerical scheme for time series clustering we investigate the conditions under which the proposed scheme allows a monotone improvement of the initial parameter guess with respect to the minimization of the discretized version of the regularized functional we also discuss the interpretation of the regularization factor in the markovian case and show its connection to metastability and exit times the computational performance of the resulting method is investigated numerically on multidimensional test data and is applied to the analysis of multidimensional historical stock market data

trellis coded modulation with multidimensional constellations trellis coded modulation schemes using four eight or 16 dimensional constellations have a number of potential advantages over the usual two dimensional schemes a smaller constituent two dimensional constellation easier tolerance to phase ambiguities and a better trade off between complexity and coding gain a number of such schemes are presented and evaluated starting with a variety of multidimensional lattices we show how to select multidimensional constellations how to partition them into subsets how to construct trellis codes using those subsets and how to map hits to constellation points simplifications of the viterbi decoding algorithm are presented we conclude that there are multidimensional trellis coded modulation schemes that perform better for the same complexity than do two dimensional schemes

trellis coded modulation on time selective fading channels a general analysis of trellis coded modulation tcm on time selective fading channels with correlated signal samples is presented gaussian quadratic forms are used to evaluate the pairwise sequence error probability the effect of interleaving is studied and it is shown that moderate interleaving with respect to the doppler frequency of the channel suffices to achieve good performance the analysis is then extended to treat non ideal estimation of the complex channel gain in the coherent case using a general linear channel estimator it is shown that differential phase shift keying dpsk and differential trellis coded modulation dtcm on correlated fading channels call be treated analytically and that the error probability of dtcm like of coherent tcm depends only on the euclidean distance of the error sequences results show that dtcm suffers a degradation of up to 3 db with respect to coherent tcm on slow fading channels but performs better on fast fading channels error floor curves are presented for dtcm for different interleaving depths the event error probability p sub e and the bit error probability p sub b of tcm approximated by truncated averaged union bounds are calculated for the codes used a comparison of the approximations of p sub b with simulation results show that the union bound is relatively loose for fading channels

convergence analysis of krylov subspace iterations with methods from potential theory krylov subspace iterations are among the best known and most widely used numerical methods for solving linear systems of equations and for computing eigenvalues of large matrices these methods are polynomial methods whose convergence behavior is related to the behavior of polynomials on the spectrum of the matrix this leads to an extremal problem in polynomial approximation theory how small can a monic polynomial of a given degree be on the spectrum this survey gives an introduction to a recently developed technique to analyze this extremal problem in the case of symmetric matrices it is based on global information on the spectrum in the sense that the eigenvalues are assumed to be distributed according to a certain measure then depending on the number of iterations the lanczos method for the calculation of eigenvalues finds those eigenvalues that lie in a certain region which is characterized by means of a constrained equilibrium problem from potential theory the same constrained equilibrium problem also describes the superlinear convergence of conjugate gradients and other iterative methods for solving linear systems

from functional analysis to iterative methods we examine condition numbers preconditioners and iterative methods for finite element discretizations of coercive pdes in the context of the fundamental solvability result the lax milgram lemma working in this hilbert space context is justified because finite element operators are restrictions of infinite dimensional hilbert space operators to finite dimensional subspaces moreover useful insight is gained as to the relationship between hilbert space and matrix condition numbers and translating hilbert space fixed point iterations into matrix computations provides new ways of motivating and explaining some classic iteration schemes in this framework the simplest preconditioner for an operator from a hilbert space into its dual is the riesz isomorphism simple analysis gives spectral bounds and iteration counts bounded independent of the finite element subspaces chosen moreover the abstraction allows us to consider not only riesz map preconditioning for convection diffusion equations in h 1 but also operators on other hilbert spaces such as planar elasticity in left h 1 right 2

sylvester tikhonov regularization methods in image restoration in this paper we consider large scale linear discrete ill posed problems where the right hand side contains noise regularization techniques such as tikhonov regularization are needed to control the effect of the noise on the solution in many applications such as in image restoration the coefficient matrix is given as a kronecker product of two matrices and then tikhonov regularization problem leads to the generalized sylvester matrix equation for large scale problems we use the global gmres method which is an orthogonal projection method onto a matrix krylov subspace we present some theoretical results and give numerical tests in image restoration

error performance of interleaved trellis coded psk modulations in correlated rayleigh fading channels the authors derive an exact and easily computed expression for the pairwise error event probability of interleaved coded psk modulations transmitted over channels with correlated rayleigh flat fading and additive white gaussian noise both coherent and differential detection are considered in the case of coded dpsk it is found that full interleaving does not necessarily provide the best error performance especially when the fading is relatively fast and when the autocorrelation function of the channel fading process exhibits an oscillating behavior for coherent detection or for differential detection in channels with relatively slow fading increasing the interleaving depth always improves the error performance in these cases an interleaving depth equivalent to one fifth to one quarter the duration of a fade cycle is almost as good as full interleaving

convergence bounds of gmres with schwarz preconditioner for the scattering problem we consider the jacobi preconditioner of the gmres method introduced by liu and jin for the scattering problem ieee trans ante prop 2002 50 132 140 we explain why it is a particular form of the schwarz preconditioner with a complete overlap and specific transmission conditions so far a superlinear convergence has been predicted by the general theory without any additional indication on the convergence rates here we establish error bounds that provide accurate convergence rates in two and three dimensions courant weyl s min max principle applied to some kernel operators together with some polynomial approximation estimates are the milestones for the proofs

error performance analysis of quadrature partial response trellis coded modulation qpr tcm in fading mobile satellite channels in order to improve the bandwidth efficiency and error performance partial response signaling prs and trellis coded modulation tcm are combined together this method is named qpr tcm whereas previous contributions have considered the performance of tcm transmitted over an additive white gaussian noise awgn channel the emphasis in this paper is on the performance of trellis coded m ary qam combined with prs in the fading environment we only consider the case where interleaving deinterleaving is employed to further combat the fading and assume that the ideal channel state information csi is available analytical upper bounds are derived using the well known transfer function bounding technique the bandwidth efficiencies are computed and the numerical results for several practical schemes are compared to each other one interesting result is that when the combined system is used on a rician fading channel the bit error probability upper bounds of the proposed 6qpr tcm and 9qpr tcm systems are better than their counterparts the 4qam tcm systems with 2 and 4 states respectively for snr values greater than a threshold which have the best error performances in the literature

a note on the superlinear convergence of gmres in the paper it is shown how the rate of convergence of the gmres method for solving a linear operator equation lambda i k u f in a hilbert space is related to the degree of compactness of k measured by the products of its singular values

estimating the non homogeneous elastic modulus distribution from surface deformations abstract we present a novel approach to solve the inverse problem in finite elasticity for the non homogeneous shear modulus distribution solely from known surface deformation fields the inverse problem is posed as a constrained optimization problem under regularization and solved utilizing the adjoint equations hypothetical measured surface displacement fields are created by inducing indentations on the exterior of the specimen these surface displacement fields are used to test the inverse strategy on a problem domain consisting of a stiff circular inclusion in a softer homogeneous background we observe that the shear modulus reconstruction as well as the shape of the circular inclusion improves with an increasing number of surface displacement fields furthermore with increasing noise level in the surface displacement field the contrast of the reconstructions decreases

the local convergence of broyden like methods on lipschitzian problems in hilbert spaces the classical local convergence analysis for broyden s method requires a finite number of real variables holder continuity of the jacobian and a rather accurate initial approximation b 0 here these three conditions are relaxed to allow for lipschitz continuous hilbert space operators that can be reasonably well approximated by a linear operator b that is close to b 0 up to an arbitrary compact perturbation to achieve local and r linear convergence broyden s method is modified by a very mild line search condition in case of a continuously differentiable system in euclidean space we obtain r superlinear convergence without restricting b 0 or requiring the jacobian to be holder continuous

superlinearly convergent pcg algorithms for some nonsymmetric elliptic systems a preconditioned conjugate gradient method is applied to finite element discretizations of some nonsymmetric elliptic systems mesh independent superlinear convergence is proved which is an extension of a similar earlier result from a single equation to systems the proposed preconditioning method involves decoupled preconditioners which yields small and parallelizable auxiliary problems

the completions of multi posets and quantum b algebras abstract multi posets as the generalization of quantum b algebras and partially ordered semigroups etc were firstly introduced and studied by rump in this paper we shall continue his work and investigate the completions of multi posets and quantum b algebras firstly we introduce the notions of the precoherent completions of a multi poset m and the algebraic consistent quantic nuclei on the power set p m f of the free semigroup of m and prove that the precoherent completions of a multi poset m is completely determined by the algebraic consistent quantic nuclei on p m f up to isomorphism moreover we give the concrete forms of the least and the largest standard precoherent completions and obtain the free quantale over a multi poset in the category of multi posets finally when the completions and consistent quantic nuclei of multi posets are applied to the cases of quantum b algebras and partially ordered semigroups several analogous results can also be obtained

constellation design for trellis coded unitary space time modulation systems we consider the problem of creating signal constellations for trellis coded unitary space time communication links where neither the transmitter nor the receiver knows the fading gains of the channel our study includes constellation design techniques for trellis coded schemes with and without parallel paths which allows us to find a tradeoff between low complexity and high performance we present a new formulation of the constellation design problem for trellis coded unitary space time modulation tcustm schemes the two key differences in our approach against those of other authors are that we not only combine the constellation design and mapping by set partitioning into one step but we also use directly the chernoff bound of the pairwise error probability as a design metric by novelly employing a theorem for the clarke subdifferential of the sum of the k largest singular values of the unitary matrix we also present a numerical optimization procedure for finding signal constellations resulting in high performance communications systems to demonstrate the advantages of our new design method we report the best constellations found for tcustm systems simulation results show that these constellations achieve a 1 db coding gain at a bit error rate of 10 4 against usually used constellations

regularization matrices determined by matrix nearness problems abstract this paper is concerned with the solution of large scale linear discrete ill posed problems with error contaminated data tikhonov regularization is a popular approach to determine meaningful approximate solutions of such problems the choice of regularization matrix in tikhonov regularization may significantly affect the quality of the computed approximate solution this matrix should be chosen to promote the recovery of known important features of the desired solution such as smoothness and monotonicity we describe a novel approach to determine regularization matrices with desired properties by solving a matrix nearness problem the constructed regularization matrix is the closest matrix in the frobenius norm with a prescribed null space to a given matrix numerical examples illustrate the performance of the regularization matrices so obtained

generalized mv algebras we generalize the notion of an mv algebra in the context of residuated lattices to include noncommutative and unbounded structures we investigate a number of their properties and prove that they can be obtained from lattice ordered groups via a truncation construction that generalizes the chang mundici functor this correspondence extends to a categorical equivalence that generalizes the ones established by d mundici and a dvurey the decidability of the equational theory of the variety of generalized mv algebras follows from our analysis

superlinear convergence of krylov subspace methods for self adjoint problems in hilbert space the conjugate gradient and minimum residual methods for self adjoint problems in hilbert space are considered linear and superlinear convergence results with respect to both q and r rates are reviewed new results on ell step q superlinear and r superlinear convergence for the minimum residual method are provided and examples are considered to underscore the relevance of a hilbert space theory

the convergence rate of the minimal residual method for the stokes problem discretisation of the classical stokes problem gives rise to symmetric indefinite matrices with eigenvalues which in a precise way are not symmetric about the origin but which do depend on a mesh size parameter convergence estimates for the conjugate residual or minimum residual iterative solution of such systems are given by best minimax polynomial approximations on an inclusion set for the eigenvalues in this paper an analytic convergence estimate for such problems is given in terms of an asymptotically small mesh size parameter

robust identification of elastic properties using the modified constitutive relation error abstract the present study concerns the identification of linear elastic material properties based on inhomogeneous tests and the use of full field measurements often based upon inverse approaches this study presents the formulation of the so called modified constitutive relation error mcre method in the context of elastostatics when dealing with uncertain data such an approach addresses the concept of the reliability of information and mainly consists in the partitioning of all the available mechanical quantities into a reliable set and a less reliable one so as to take into account the measurement uncertainties and the error made on the constitutive equation into the formulation and then allows to identify the sought material properties the method is split in two steps the first one consists in defining admissible mechanical fields from all the theoretical and experimental data for a fixed set of mechanical properties this is made by the minimization of a criterion allowing a compromise between the constitutive equation and the measurements adequacy then the second step consists in the identification of the sought material properties and takes the form of minimizing a cost function defined by using the above admissible mechanical fields a comparison with the finite element model updating femu method was performed on some numerical examples where realistic perturbations were added this comparison showed that the mcre method is more robust towards perturbations for similar input data moreover the proposed method only deals with the available information and does not need additional hypotheses to calculate the mechanical quantities eventually the method was applied to the identification of the shear modulus of an organic matrix composite from experimental data

i q tcm reliable communication over the rayleigh fading channel close to the cutoff rate this paper presents some trellis codes that provide high coding gain to channels with slow non frequency selective rayleigh fading it is shown that the use of two encoders in parallel used to specify the in phase and quadrature components of the transmitted signal results in greater minimum time diversity than the conventional design in which a single encoder is used using this approach which we label i q tcm codes with bandwidth efficiencies of 1 2 and 3 bits s hz are described for various constraint lengths the performance of these codes is bounded analytically and approximated via simulation the results show a large improvement in the bit error rate ber when compared with conventional trellis coded modulation tcm schemes when perfect channel state information csi is available to the receiver indeed when this approach is applied to channels with independent rayleigh fading the resulting coding gain is close to that implied by the cutoff rate limit even for only moderately complex systems the proposed codes are also simulated under less ideal assumptions for instance results for a 1 bit s hz iq tcm code without csi show a significant gain over conventional coding finally simulations over channels with correlated fading were undertaken it is concluded that an interleaver span of 4 spl nu yields performance close to what is achieved with ideal interleaving

arnoldi methods for image deblurring with anti reflective boundary conditions image deblurring with anti reflective boundary conditions and a non symmetric point spread function is considered several iterative methods based on krylov subspace projections as well as arnoldi tikhonov regularization methods with reblurring right or left preconditioners are compared the aim of the preconditioner is not to accelerate the convergence but to improve the quality of the computed solution and to increase the robustness of the regularization method right preconditioning in conjunction with methods based on the arnoldi process are found to be robust and give high quality restorations in particular when the observed image is contaminated by motion blur our new method is much more effective than other approaches described in the literature such as range restricted arnoldi methods and the conjugate gradient method applied to the normal equations implemented with the reblurring approach

the generalized finite difference method for the inverse cauchy problem in two dimensional isotropic linear elasticity abstract in this study the generalized finite difference method gfdm was used to stably and accurately solve two dimensional 2d inverse cauchy problems in linear elasticity by using the navier equations in cauchy problems overdetermined boundary conditions are imposed on parts of the boundary whereas there are missing boundary conditions on some parts of the boundary in cauchy problems conventional numerical methods generally generate highly ill conditioned matrices and thus provide unstable numerical solutions moreover even if a slight noise is added in the boundary conditions numerical errors are evidently magnified the gfdm one of the most promising meshless methods and an extension of the classical finite difference method can avoid time consuming tasks of mesh generation and numerical quadrature the gfdm was applied in this study to stably solve the 2d cauchy problems in linear elasticity and four numerical examples are provided to illustrate the consistency and accuracy of the presented meshless numerical scheme moreover the stability of the presented scheme for inverse cauchy problems was proved by adding noise into the boundary conditions

the design of trellis coded mpsk for fading channels performance criteria it has been well established that the appropriate criterion for optimum trellis coded modulation design on the additive white gaussian noise channel is maximization of the free euclidean distance it is shown that when the trellis coded modulation is used on a rician fading channel with interleaving deinterleaving the design of the code of optimum performance is guided by other factors in particular the length of the shortest error event path and the product of branch distances possibly normalized by the euclidean distance of the path along the path although maximum free distance d sub free is still an important consideration it plays a less significant role the more severe the fading is on the channel these considerations lead to the definition of a new distance measure of optimization of trellis codes transmitted over rician fading channels if no interleaving deinterleaving is used then once again the design of the trellis code is guided by maximizing d sub free