the congruence class of the solutions of some matrix equations the congruence class of a least square solution for the following matrix equations ax b a xa d axb dand axxb ef is presented also we derive necessary and sufficient conditions for the existence of a least square solution and present a general form of such solutions using the singular value decomposition svd and generalized singular value decomposition gsvd

parameter identification of nonlinear aeroelastic system with time delayed feedback control in this paper an enhanced response sensitivity approach is proposed for parameter identification of nonlinear time delay aeroelastic systems two common aeroelastic models are investigated namely

a new l curve for ill posed problems the truncated singular value decomposition is a popular method for the solution of linear ill posed problems the method requires the choice of a truncation index which affects the quality of the computed approximate solution this paper proposes that an l curve which is determined by how well the given data right hand side can be approximated by a linear combination of the first few left singular vectors or functions be used as an aid for determining the truncation index

on g inverses of a bordered matrix revisited abstract in this article we study the structure and properties of g inverse m of the bordered matrix m a b c 0 which is partitioned conforming with m m d 1 d 2 d 3 d 4 by applying the multiple quotient singular value decomposition qq svd from the structure of m we discuss the relations among d1 d2 d3 and d4 and derive equivalent conditions for m to be a bordered matrix by studying d1 in m we obtain some equivalent conditions for d1 to be a g inverse of a

reverse order law for reflexive generalized inverses of products of matrices abstract the relationships between generalized inverses of the product of two matrices a b and the product of generalized inverses of a b have been studied in the literature by applying the product singular value decomposition p svd in this paper we derive equivalent conditions for b 1 2 a 1 2 ab 1 2 ab 1 2 b 1 2 a 1 2 b 1 2 a 1 2 ab 1 2 and equivalent conditions for ab 1 b 1 a 1

on the early history of the singular value decomposition this paper surveys the contributions of five mathematicians eugenio beltrami 1835 1899 camille jordan 1838 1921 james joseph sylvester 1814 1897 erhard schmidt 1876 1959 and hermann weyl 1885 1955 who were responsible for establishing the existence of the singular value decomposition and developing its theory

towards a generalized singular value decomposition we suggest a form for and give a constructive derivation of the generalized singular value decomposition of any two matrices having the same number of columns we outline its desirable characteristics and compare it to an earlier suggestion by van loan siam j numer anal 13 1976 pp 76 83 the present form largely follows from the work of van loan but is slightly more general and computationally more amenable than that in the paper cited we also prove a useful extension of a theorem of stewart siam rev 19 1977 pp 634 662 on unitary decompositions of submatrices of a unitary matrix

rational extrapolation for the pagerank vector an important problem in web search is to determine the importance of each page from the mathematical point of view this problem consists in finding the nonnegative left eigenvector of a matrix corresponding to its dominant eigenvalue 1 since this matrix is neither stochastic nor irreducible the power method has convergence problems so the matrix is replaced by a convex combination depending on a parameter c with a rank one matrix its left principal eigenvector now depends on c and it is the pagerank vector we are looking for however when c is close to 1 the problem is ill conditioned and the power method converges slowly so the idea developed in this paper consists in computing the pagerank vector for several values of c and then to extrapolate them by a conveniently chosen rational function at a point near 1 the choice of this extrapolating function is based on the mathematical expression of the pagerank vector as a function of c numerical experiments end the paper

the backus gilbert method and their minimum norm solution abstractthis paper has two objectives one is to review the backus gilbert bg method backus and gilbert investigate continuous inverse problems in a radially symmetric earth using an approach completely different from that of standard inversion methods if m is an earth property of interest the bg method provides average values of m over some radial intervals if an interval w is relatively short and centered near a particular radius r0 the bg average will be a local average of m near r0 with a resolving length of w backus and gilbert also introduce the concept of trade off between resolution and error which is essential in inverse theory regardless of the inversion method in spite of its importance inverse theory texts neither describe the bg method in full nor show how to apply it in all its generality because the three papers that introduce the bg method are mathematically difficult this paper provides background material and a detailed derivation of the method as well as two completely wor

inverse geometry heat transfer problem based on a radial basis functions geometry representation summary we present a methodology for solving a nonlinear inverse geometry heat transfer problem where the observations are temperature measurements at points inside the object and the unknown is the geometry of the volume where the problem is de ned the representation of the geometry is based on radial basis functions rbfs and the nonlinear inverse problem is solved using the iteratively regularized gauss newton method in our work we consider not only the problem with no geometry restrictions but also the bound constrained problem the methodology is used for the industrial application of estimating the location of the 1150 c isotherm in a blast furnace hearth based on measurements of the thermocouples located inside it we validate the solution of the algorithm against simulated measurements with different levels of noise and study its behavior on different regularization matrices finally we study the error behavior of the solution copyright c 2004 john wiley sons ltd

history and generality of the cs decomposition abstract it is almost a quarter of a century since chandler davis and william kahan brought together the key ideas of what stewart later completed and defined to be the cs decomposition csd of a partitioned unitary matrix this paper outlines some germane points in the history of the csd pointing out the contributions of jordan of davis and kahan and of stewart and the relationship of the csd to the direct rotation of davis and kato the paper provides an easy to memorize constructive proof of the csd reviews one of its important uses and suggests a motivation for the csd which emphasizes how generally useful it is it shows the relation between the csd and generalized singular value decompositions and points out some useful nullity properties one form of the csd trivially reveals finally it shows how via the qr factorization the csd can be used to obtain interesting results for partitioned nonsingular matrices we suggest the csd be taught in its most general form with no restrictions on the two by two partition and initially with no mention of angles between subspaces

turbo spc codes this letter is concerned with a family of modified turbo type codes referred to as turbo spc single parity check codes a technique based on the spc code is introduced to replace puncturing for rate adjustment a noticeable feature of the proposed scheme is the significantly reduced decoding complexity compared with the standard punctured turbo code the cost reduction factor becomes more noticeable as rate increases over ten times for rate spl rarr 1 the error rate floor problem known to turbo codes can also be improved using the proposed scheme for moderate to high rates performances of about 0 5 db from the theoretical limits at ber 10 sup 5 have been observed for turbo spc codes

multi parameter tikhonov regularization and model function approach to the damped morozov principle for choosing regularization parameters in this paper we study the multi parameter tikhonov regularization method which adds multiple different penalties to exhibit multi scale features of the solution an optimal error bound of the regularization solution is obtained by a priori choice of multiple regularization parameters some theoretical results of the regularization solution about the dependence on regularization parameters are presented then an a posteriori parameter choice i e the damped morozov discrepancy principle is introduced to determine multiple regularization parameters five model functions i e two hyperbolic model functions a linear model function an exponential model function and a logarithmic model function are proposed to solve the damped morozov discrepancy principle furthermore four efficient model function algorithms are developed for finding reasonable multiple regularization parameters and their convergence properties are also studied numerical results of several examples show that the damped discrepancy principle is competitive with the standard one and the model function algorithms are efficient for choosing regularization parameters

construction of low density parity check codes based on balanced incomplete block designs this correspondence presents a method for constructing structured regular low density parity check ldpc codes based on a special type of combinatoric designs known as balance incomplete block designs codes constructed by this method have girths at least 6 and they perform well with iterative decoding furthermore several classes of these codes are quasi cyclic and hence their encoding can be implemented with simple feedback shift registers

sirt and cg type methods for the iterative solution of sparse linear least squares problems abstract sirt and cg type methods have been successfully employed for the approximate solution of least squares problems arising in tomography in this paper we study and compare their convergence and regularization properties it is pointed out that sirt methods apply an uncontrollable implicit rescaling which affects the statistical characteristics of the system whereas cg type methods do not for a large class of model problems it is shown that virtually the same solutions as obtained by sirt methods can be obtained by applying a cg type method to a properly rescaled system but with an amount of work proportional to the square root of the amount of work with sirt

extrapolation techniques for ill conditioned linear systems in this paper the regularized solutions of an ill conditioned system of linear equations are computed for several values of the regularization parameter lambda then these solutions are extrapolated at lambda 0 by various vector rational extrapolations techniques built for that purpose these techniques are justified by an analysis of the regularized solutions based on the singular value decomposition and the generalized singular value decomposition numerical results illustrate the effectiveness of the procedures

simultaneous decomposition of quaternion matrices involving ź hermicity with applications let r and h m n stand respectively for the real number field and the set of all m n matrices over the real quaternion algebra h a 0 a 1 i a 2 j a 3 k i 2 j 2 k 2 ijk 1 a 0 a 1 a 2 a 3 r for i j k a real quaternion matrix a h n n is said to be hermitian if a a where a a and a stands for the conjugate transpose of a arising in widely linear modeling we present a simultaneous decomposition for a set of nine real quaternion matrices involving hermicity with compatible sizes a i h p i t i b i h p i t i 1 and c i h p i p i where ci are hermitian matrices i 1 2 3 as applications of the simultaneous decomposition we give necessary and sufficient conditions for the existence of an hermitian solution to the system of coupled real quaternion matrix equations a i x i a i b i x i 1 b i c i i 1 2 3 and provide an expression of the general hermitian solutions to this system moreover we derive the rank bounds of the general hermitian solutions to the above mentioned system using ranks of the given matrices ai bi and ci as well as the block matrices formed by them finally some numerical examples are given to illustrate the results of this paper

a simultaneous decomposition for seven matrices with applications abstract let h m n be the set of all m n matrices over the quaternion algebra h in this paper we construct a simultaneous decomposition for seven matrices with compatible sizes a h m n b h m p 1 c h m p 2 d h m p 3 e h q 1 n f h q 2 n and g h q 3 n as applications of the simultaneous matrix decomposition we give some solvability conditions general solutions as well as the range of ranks of the general solutions to the following two generalized sylvester matrix equations b x e c y f d z g a and b x w e c y f d z g a where a b c d e f and g are given quaternion matrices moreover we provide some numerical examples to illustrate the results of this paper

simplified gsvd computations for the solution of linear discrete ill posed problems the generalized singular value decomposition gsvd often is used to solve tikhonov regularization problems with a regularization matrix without exploitable structure this paper describes how the standard methods for the computation of the gsvd of a matrix pair can be simplified in the context of tikhonov regularization also other regularization methods including truncated gsvd are considered we compare the computational efforts required by the simplified gsvd method and the a weighted generalized inverse introduced by elden

the 2 norm of random matrices abstract numerical experiments show that it is possible to derive simple estimates for the expected 2 norm of random matrices a with elements from a normal distribution with zero mean and standard deviation and from a poisson distribution with mean value these estimates are max m n 2 max m n and e 2 mn respectively where m and n are the dimensions of a

flat top footprint pattern synthesis through the design of arbitrary planar shaped apertures the problem of generating a flat top main beam with an arbitrary footprint for array elements placed in an arbitrary planar aperture is considered in this paper some simplifying properties of the bessel functions encourages the general framework of the paper to encompass patterns produced by circular aperture and eventually generalize it to arbitrary aperture geometries in this regard two synthesis methods are presented the first method is based on the use of the rayleigh quotient to obtain constant phase array patterns hence a class of generally linear phase patterns can be considered the second approach is based on power pattern synthesis where there is no restriction on the phase of the pattern hence it provides us with greater flexibility the nonlinear problem is appropriately modeled and formulated for amenable performance these two new methods can exhibit a significant reduction in the number of unknown parameters and high flexibility in shaping the desired main beam by arbitrary lattice geometry

a tree of generalizations of the ordinary singular value decomposition abstract it is shown how to generalize the ordinary singular value decomposition of a matrix into a combined factorization of any number of matrices we propose to call these factorizations generalized singular value decompositions for two matrices this reduces to the product and quotient singular value decompositions one of the factorizations for three matrices is the restricted singular value decomposition these generalizations form a tree of factorizations where at level k for k matrices there are 2 k factorizations not all of which are independent the different levels are related to each other in a recursive fashion any generalized singular value decomposition for k matrices can be constructed from a decomposition for k 1 matrices this results in an inductive proof which uses only the ordinary singular value decomposition several examples are analysed in detail

a note on the reverse order law for reflexive generalized inverse of multiple matrix products the reverse order law for reflexive generalized inverses of multiple matrix products was introduced and discussed in m wei reverse order laws for generalized inverse of multiple matrix products linear algebra appl 293 1999 273 288 there the author derived some necessary and sufficient conditions for the reverse order lawa n 1 2 a n 1 1 2 a 1 1 2 a 1a 2 a n 1 2 by applying the product singular value decomposition p svd in this note we revisited this reverse order law by using the extremal rank relations of generalized schur complements and a new simpler equivalent condition is obtained in terms of only the ranks of the known matrices

on a generalization of reginska s parameter choice rule and its numerical realization in large scale multi parameter tikhonov regularization abstract a crucial problem concerning tikhonov regularization is the proper choice of the regularization parameter this paper deals with a generalization of a parameter choice rule due to reginska 1996 31 analyzed and algorithmically realized through a fast fixed point method in bazan 2008 3 which results in a fixed point method for multi parameter tikhonov regularization called mfp like the single parameter case the algorithm does not require any information on the noise level further combining projection over the krylov subspace generated by the golub kahan bidiagonalization gkb algorithm and the mfp method at each iteration we derive a new algorithm for large scale multi parameter tikhonov regularization problems the performance of mfp when applied to well known discrete ill posed problems is evaluated and compared with results obtained by the discrepancy principle the results indicate that mfp is efficient and competitive the efficiency of the new algorithm on a super resolution problem is also illustrated

some matrix nearness problems suggested by tikhonov regularization abstract the numerical solution of linear discrete ill posed problems typically requires regularization i e replacement of the available ill conditioned problem by a nearby better conditioned one the most popular regularization methods for problems of small to moderate size are tikhonov regularization and truncated singular value decomposition tsvd by considering matrix nearness problems related to tikhonov regularization several novel regularization methods are derived these methods share properties with both tikhonov regularization and tsvd and can give approximate solutions of higher quality than either one of these methods

fault reconstruction for takagi sugeno fuzzy systems via learning observers abstractthis paper addresses the problem of observer based fault reconstruction for takagi sugeno fuzzy systems two types of fuzzy learning observers are constructed to achieve simultaneous reconstruction of system states and actuator faults stability and convergence of the proposed observers are proved using lyapunov stability theory and necessary conditions for the existence of the observers are further discussed the design of fuzzy learning observers can be formulated in terms of a series of linear matrix inequalities that can be conveniently solved using convex optimisation technique a single link flexible manipulator is employed to verify the effectiveness of the proposed fault reconstructing approaches

on the solvability of the constrained lyapunov problem this paper considers system theoretic conditions for the solvability of the so called constrained lyapunov problem for nonsquare systems these problems commonly appear in the control systems literature both a static output feedback problem and an observer problem are considered the basis for the work described in this paper is a new canonical form that simplifies the analysis and deals with the equality constraint in a simple way

multi parameter regularization techniques for ill conditioned linear systems when a system of linear equations is ill conditioned regularization techniques provide a quite useful tool for trying to overcome the numerical inherent difficulties the ill conditioned system is replaced by another one whose solution depends on a regularization term formed by a scalar and a matrix which are to be chosen in this paper we consider the case of several regularizations terms added simultaneously thus overcoming the problem of the best choice of the regularization matrix the error of this procedure is analyzed and numerical results prove its efficiency

multi parameter regularization and its numerical realization in this paper we propose and analyse a choice of parameters in the multi parameter regularization of tikhonov type a modified discrepancy principle is presented within the multi parameter regularization framework an order optimal error bound is obtained under the standard smoothness assumptions we also propose a numerical realization of the multi parameter discrepancy principle based on the model function approximation numerical experiments on a series of test problems support theoretical results finally we show how the proposed approach can be successfully implemented in laplacian regularized least squares for learning from labeled and unlabeled examples

stability of the notion of approximating class of sequences and applications given an approximating class of sequences b n m n m for a n n we prove that b n m n m x being the pseudo inverse of moore penrose is an approximating class of sequences for a n n where a n n is a sparsely vanishing sequence of matrices a n of size d n with d k d q for k q k email protected n as a consequence we extend distributional spectral results on the algebra generated by toeplitz sequences by including the pseudo inversion operation in the case where the sequences that are pseudo inverted are distributed as sparsely vanishing symbols applications to preconditioning and a potential use in image signal restoration problems are presented

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

reverse order laws for least squares g inverses and minimum norm g inverses of products of two matrices in this paper we derive equivalent conditions for reverse order laws of least squares g inverses and minimum norm g inverses of product of two matrices a and b by applying the product singular value decomposition p svd

two sided coupled generalized sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices abstract in this paper we investigate and analyze in detail the structure and properties of a simultaneous decomposition for fifteen matrices a i c p i t i b i c s i q i c i c p i t i 1 d i c s i 1 q i and e i c p i q i i 1 2 3 we show that from this simultaneous decomposition we can derive some necessary and sufficient conditions for the existence of a solution to the system of two sided coupled generalized sylvester matrix equations with four unknowns a i x i b i c i x i 1 d i e i i 1 2 3 apart from proving an expression for the general solutions to this system we derive the range of ranks of these solutions using the ranks of the given matrices a i b i c i d i and e i we provide some numerical examples to illustrate our results moreover we present a similar approach to consider the simultaneous decomposition for 5k matrices and the system of k two sided coupled generalized sylvester matrix equations with k 1 unknowns a i x i b i c i x i 1 d i e i i 1 k k 4 the main results are also valid over the real number field and the real quaternion algebra

equivalent conditions for generalized inverses of products abstract the relationships between generalized inverses of the product of two matrices a b and the product of generalized inverses of a b have been studied in the literature and equivalent conditions for b 1 a 1 ab 1 have been reported by applying the product singular value decomposition we derive more equivalent conditions for b 1 a 1 ab 1 and derive equivalent conditions for b 1 a 1 ab 1

on a variational formulation of the qsvd and the rsvd abstract recently m t chu r f funderlic and g h golub siam j matrix anal appl 18 1997 1082 1092 presented a variational formulation for the quotient singular value decomposition qsvd of two matrices a r n m c r p m which is a generalization to two matrices of the ordinary singular value decomposition svd and characterizes the role of two orthogonal matrices in qsvd in this paper we give an alternative derivation of this variational formulation and extend it to establish an analogous variational formulation for the restricted singular value decomposition rsvd of a matrix triplet a r n m b r n l c r p m which provides a new understanding of the orthogonal matrices appearing in this decomposition

on least squares g inverses and minimum norm g inverses of a bordered matrix abstract by applying the restricted singular value decomposition r svd qq svd in this article we derive structures of least squares g inverses and minimum norm g inverses of a bordered matrix m a b c 0 we also obtain the specific formulation of the pesudo inverse m

fuzzy model based fault tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults this paper addresses the problem of fault estimation and fault tolerant control for a class of takagi sugeno t s fuzzy ito stochastic systems subject to simultaneously sensor and actuator faults the main difficulty in this study is that sensor faults actuator faults and stochastic noise that are governed by brownian motion are taken into simultaneous consideration in a unified framework and traditional fault tolerant approaches are not effective to solve this research issue a new descriptor fuzzy sliding mode observer approach is presented in this paper to obtain the simultaneous estimates of system state sensor fault and actuator fault vectors based on the state estimates an observer based fault tolerant control ftc scheme is developed to stabilize the resulting closed loop system finally a simulation example is provided to show the effectiveness of the proposed fault tolerant approach

recovering the density of a string from only lowest frequency data a classical inverse problem is can you hear the density of a string clamped at both ends the answer as narrowly stated is negative one has to give an additional data sequence such as the energy in each mode norming constants or information on the string slope at the endpoints or alternatively change the boundary conditions and obtain the new frequencies what if neither of these options is possible one solution recently proposed was to add a known mass density and remeasure the dirichlet spectrum w rundell and p e sacks siam j appl math 73 2013 pp 1020 1037 in this work we take a related approach we are able to add any number of known mass densities but we can only measure the fundamental frequency that is the lowest eigenvalue in each case we will show that our problem can be closely approximated by a related problem for which there is uniqueness and we discuss a suite of reconstruction methods

a geometric approach to nonlinear fault detection and isolation we present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems a necessary condition for the problem to be solvable is derived in terms of an unobservability distribution which is computable by means of suitable algorithms the existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an observable quotient subsystem unaffected by all fault signals but one for this subsystem a fault detection filter is designed

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

asymptotic theory of filtering for linear operator equations with discrete noisy data on considere les equations integrales de fredholm de premiere espece a noyaux continus avec echantillonnage des donnees et alteration par le bruit blanc on etablit une condition suffisante de convergence des methodes de filtrage

square smoothing regularization matrices with accurate boundary conditions this paper is concerned with the solution of large scale linear discrete ill posed problems the determination of a meaningful approximate solution of these problems requires regularization we discuss regularization by the tikhonov method and by truncated iteration the choice of regularization matrix in tikhonov regularization may significantly affect the quality of the computed approximate solution the present paper describes the construction of square regularization matrices from finite difference equations with a focus on the boundary conditions the regularization matrices considered have a structure that makes them easy to apply in iterative methods including methods based on the arnoldi process numerical examples illustrate the properties and effectiveness of the regularization matrices described

on the numerical recovery of a holomorphic mapping from a finite set of approximate values the least squares approach for the recovery of a holomorphic mapping from given perturbed nodal values is considered the mapping is assumed to be a priori bounded by a known quantity so that the recovery problem is well posed the present analysis shows that for nodes that are the zeroes of jacobi polynomials a quasioptimal algorithm results with a fairly moderate number of nodes the analysis also takes into account the effect of the numerical linear algebra involved some numerical experiments are presented

computing the cs and the generalized singular value decompositions if the columns of a matrix are orthonormal and it is partitioned into a 2 by 1 block matrix then the singular value decompositions of the blocks are related this is the essence of the cs decomposition the computation of these related svd s requires some care stewart has given an algorithm that uses the linpack svd algorithm together with a jacobitype clean up operation on a cross product matrix our technique is equally stable and fast but avoids the cross product matrix the simplicity of our technique makes it more amenable to parallel computation on systolic type computer architectures these developments are of interest because a good way to compute the generalized singular value decomposition of a matrix pair a b is to compute the cs decomposition of a certain orthogonal column matrix related toa andb

reverse order laws for generalized inverses of multiple matrix products abstract in this article we study reverse order laws for generalized inverses and reflexive generalized inverses of the products of multiple matrices a 1 a n and the products of generalized inverses and reflexive generalized inverses of a n a 1 by applying the multiple product singular value decomposition we obtain necessary and sufficient conditions for one side inclusion relation of reverse order law for generalized inverses and necessary and sufficient conditions of reverse order law for reflexive generalized inverses

optimally scaled vector regularization method to solve ill posed linear problems instead of the tikhonov regularization method which with a scalar being the regularization parameter liu et al 1 have proposed a novel regularization method with a vector as being the regularization parameter as a continuation we further propose an optimally scaled vector regularization method osvrm to solve the ill posed linear problems which is better than the tikhonov regularization method the presently proposed vector regularization method is shown to be well conditioning to overcome the ill posedness of the linear equations system the osvrm causes a significant improvement of stability and accuracy in the numerical solution of ill posed linear problem and its convergence speed is as fast as by solving the well posed linear problem some tests of the linear inverse problems confirm the efficiency and accuracy of the osvrm

complex rotary codes revisited a low complexity high performance decoding approach in this paper based on a belief propagation decoding strategy a class of generalized parity check codes called complex rotary codes is investigated it is shown that by using iterative sum product decoding the complex rotary codes have a much lower decoding complexity than turbo codes but have almost the same performance for the high code rate and short frame case frame length 500 bits it is also shown that the prime block size of complex rotary codes is essential to achieve better performance because of its uniform checking characteristic

single parity check product codes this paper considers the performance of iteratively decoded single parity check spc multidimensional product codes in an additive white gaussian noise channel asymptotic performance bounds are compared to simulation results a new code structure based on spc product codes is introduced this structure involves interleaving between the encoding of each dimension in the product code an analysis of the weight distribution is used to explain the good performance results for these randomly interleaved spc product codes

a rational arnoldi approach for ill conditioned linear systems for the solution of full rank ill posed linear systems a new approach based on the arnoldi algorithm is presented working with regularized systems the method theoretically reconstructs the true solution by means of the computation of a suitable function of matrix in this sense the method can be referred to as an iterative refinement process numerical experiments arising from integral equations and interpolation theory are presented finally the method is extended to work in connection with the standard tikhonov regularization with the right hand side contaminated by noise

constructing the physical parameters of a damped vibrating system from eigendata abstract in this paper we consider the inverse problem for a discrete damped mass spring system where the mass damping and stiffness matrices are all symmetric tridiagonal we first show that the model can be constructed from two real eigenvalues and three real eigenvectors or two complex conjugate eigenpairs and a real eigenvector then we study the general under determined and over determined problems in particular we provide the sufficient and necessary conditions on the given two real or complex conjugate eigenpairs so that the under determined problem has a physical solution however for large model order the construction from these data may be sensitive to perturbations to reduce the sensitivity we propose the minimum norm solution over the under determined noisy data and the least squares solution to the over determined measured data we also discuss the physical realizability of the required model by the positivity constrained regularization method for the ill posed under determined problem and the least squares optimization problems with positivity constraints for the ill posed over determined problem finally we give simple numerical examples to illustrate the effectiveness of our methods

parameter choice strategies for multipenalty regularization the widespread applicability of the multipenalty regularization is limited by the fact that theoretically optimal rate of reconstruction for a given problem can be realized by a one parameter counterpart provided that relevant information on the problem is available and taken into account in the regularization in this paper we explore the situation where no such information is given but still accuracy of optimal order can be guaranteed by employing multipenalty regularization our focus is on the analysis and the justification of an a posteriori parameter choice rule for such a regularization scheme first we present a modified version of the discrepancy principle within the multipenalty regularization framework as a consequence we provide a theoretical justification to the multipenalty regularization scheme equipped with the a posteriori parameter choice rule we then establish a fast numerical realization of the proposed discrepancy principle based on a model function approximation finally we pro

state and input estimation for a class of uncertain systems we consider here the problem of state and input estimation for a class of uncertain systems which consist of a nominally linear part and an uncertain nonlinear time varying part which can be regarded as a state dependent time varying input we obtain a lyapunov type characterization of the assumptions commonly found in the literature on this problem using this characterization we obtain estimators which using only a measured output can asymptotically estimate to any desired accuracy the system state and the input

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

relations between svd and gsvd of discrete regularization problems in standard and general form abstract we consider an algorithm due to elden that transforms general discrete regularization problems into standard form we derive a simple relationship between the svd associated with the standard form problem and the gsvd associated with the general problem and we discuss the accuracy of the gsvd computed via this transformation

robust observer design for unknown inputs takagi sugeno models this paper deals with the observer design for takagi sugeno t s fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system sufficient conditions to design an unknown input t s observer are given in linear matrix inequality lmi terms both continuous time and discrete time cases are studied relaxations are introduced by using intermediate variables extension to the case of unmeasured decision variables is also given a numerical example is given to illustrate the effectiveness of the given results

extremal ranks of matrix expression of a bxc with respect to hermitian matrix abstract the extremal ranks of matrix expression of a bxc with respect to x h x have been discussed by applying the quotient singular value decomposition q svd and some rank equalities of matrices in this paper

on the structure and geometry of the product singular value decomposition the product singular value decomposition is a factorization of two matrices which can be considered as a generalization of the ordinary singular value decomposition at the same level of generality as the quotient generalized singular value decomposition a constructive proof of the product singular value decomposition is provided which exploits the close relation with a symmetric eigenvalue problem several interesting properties are established the structure and the non uniqueness properties of the so called contragredient transformation which appears as one of the factors in the product singular value decomposition are investigated in detail finally a geometrical interpretation of the structure is provided in terms of principal angles between subspaces

computing the generalized singular values vectors of large sparse or structured matrix pairs we present a numerical algorithm for computing a few extreme generalized singular values and corresponding vectors of a sparse or structured matrix pair a b the algorithm is based on the cs decomposition and the lanczos bidiagonalization process at each iteration step of the lanczos process the solution to a linear least squares problem with a rm t b rm t rm t as the coefficient matrix is approximately computed and this consists the only interface of the algorithm with the matrix pair a b numerical results are also given to demonstrate the feasibility and efficiency of the algorithm

forward order law for g inverses of the product of two matrices abstract in this paper we derive equivalent conditions for a b ab by the method of maximal rank and thus we obtain equivalent conditions for the forward order laws of the product of two matrices

a modified tikhonov regularization method tikhonov regularization and truncated singular value decomposition tsvd are two elementary techniques for solving a least squares problem from a linear discrete ill posed problem based on these two techniques a modified regularization method is proposed which is applied to an arnoldi based hybrid method theoretical analysis and numerical examples are presented to illustrate the effectiveness of the method

more comments on c p we discuss the interpretation of c p plots and show how they can be calibrated in several ways we comment on the practice of using the display as a basis for formal selection of a subset regression model and extend the range of application of the device to encompass arbitrary linear estimates of the regression coefficients for example ridge estimates