on the membership of hankel operators in a class of lorentz ideals abstract recall that the lorentz ideal c p is the collection of operators a satisfying the condition a p j 1 j p 1 p s j a consider hankel operators h f h 2 s l 2 s d h 2 s where h 2 s is the hardy space on the unit sphere s in c n in this paper we characterize the membership h f c p 2 n p

upper and lower bounds of the misadjustment in the lms algorithm the misadjustment is a dimensionless measure of the difference between the optimal weiner performance and the actual performance of the lms least mean squares algorithm this difference is attributed to the gradient noise in the adaptive process present estimates relate the misadjustment to the convergence gain and the trace of the autocorrelation matrix the authors establish tighter lower bounds on the estimate of this misadjustment an upper bound on the misadjustment as a function of the convergence gain is found

performance advantage of complex lms for controlling narrow band adaptive arrays in narrow band adaptive array applications the mean square convergence of the discrete time real least mean square lms algorithm is slowed by image frequency noises generated in the lms loops the complex lms algorithm proposed by widrow et al is shown to eliminate these noises yielding convergence of the mean squared error mse at slightly over twice the rate this paper includes a comprehensive analysis of the mse of adaptation for lms the analysis is based upon the method developed in the 1968 dissertation by k d senne and it represents the most complete treatment of the subject published to date

a relaxation procedure for domain decomposition methods using finite elements we present the convergence analysis of a new domain decomposition technique for finite element approximations this technique was introduced in 11 and is based on an iterative procedure among subdomains in which transmission conditions at interfaces are taken into account partly in one subdomain and partly in its adjacent no global preconditioner is needed in the practice but simply single domain finite element solvers are required an optimal strategy for an automatic selection of a relaxation parameter to be used at interface subdomains is indicated applications are given to both elliptic equations and incompressible stokes equations

iterative analysis of the steady state weight fluctuations in lms type adaptive filters an iterative method is proposed for the analysis of the steady state weight fluctuations in an lms type adaptive fir filter without the widely used independence assumption a power series of the weight error correlation matrix is derived in terms of the stepsize some new effects are observed e g a decrease of the weight fluctuations along the tapped delay line

une minoration de la norme de l operateur de cauchy sur les graphes lipschitziens it was shown by t murai that the norm of the operator defined by the cauchy kernel on the graph of a lipschitz function a is less than c 1 iiatlioo l 2 we use garnett s example to show that this estimate is optimal

analysis of error gradient adaptive linear estimators for a class of stationary dependent processes in many applications the training data to be processed by an adaptive linear estimator can be assumed to have a finite correlation length an exact analysis for this class of problems that yields the coefficient bias coefficient correlation matrix and mean square estimation error is obtained via a stochastic imbedding procedure a power series expansion in the gain parameter is used to obtain simplified expressions of order one for the above statistical moments these new expressions are shown to contain the terms that would result from an analysis based upon the assumption of independent training data plus additional terms arising from data correlation algorithm convergence properties are studied by identifying the appropriate matrix eigenvalues from the first order theory

steering an adaptive antenna array by the simplified kalman filter adaptive antenna arrays controlled by the kalman filter excel in high rate of convergence low misadjustment and independence on a priori information about interference statistics high computational requirements and potential numerical non stability are drawbacks of the kalman s steering the author describes a way of reducing computational requirements and improving numerical stability of the steering algorithm based on a kalman filter rate of convergence and misadjustment of the resultant algorithm simplified kalman filter skf are better in comparison with the optimal lms and worse than the pure kalman filter computational requirements of the skf are approximately three times higher in comparison with the lms skf does not require any a priori information about interference statistics and is totally numerically stable

s numbers of singular integrals for the invariance of absolutely continuous spectra in fractional dimensions an important consequence of the kato rosenblum theorem in abstract scattering theory 5 81 is the invariance up to unitary equivalence of absolutely continuous spectra under trace class perturbations the extension of this fact to higher integral dimensions was given in lo a careful inspection of trace class scattering theory reveals the crucial role of l2 boundedness of the hilbert transform in the one dimensional case in the n dimensional generalization this is replaced by the asymptotics of fourier coefficients of 2 1 x k c n 1 11 2 on the torus or equivalently by the asymptotics of s numbers of corresponding singular integrals the general functional analysis machinery developed in 9 lo for studying normed ideal perturbations of systems of hilbert space operators reduces this kind of operator theory questions to questions about the existence or non existence of quasicentral approximate units relative to normed ideals the existence of quasicentral approximate units in turn is related to commutator questions 11 j for related considerations in the quasidiagonality context see 7 the natural operators to examine are then singular integral operators in this paper we consider the fractional dimensional case the natural singular integral problem in this case is to estimate the s numbers of singular integrals with kernels yjl lx 1 in l p where 1 is a compactly supported probability measure on w of fractional dimension like hausdorff measure restricted to suitable compacta the results we

a tree structured piecewise linear adaptive filter the authors propose and analyze a novel architecture for nonlinear adaptive filters these nonlinear filters are piecewise linear filters obtained by arranging linear filters and thresholds in a tree structure a training algorithm is used to adaptively update the filter coefficients and thresholds at the nodes of the tree and to prune the tree the resulting tree structured piecewise linear adaptive filter inherits the robust estimation and fast adaptation of linear adaptive filters along with the approximation and model fitting properties of tree structured regression models a rigorous analysis of the training algorithm for the tree structured filter is performed some techniques are developed for analyzing hierarchically organized stochastic gradient algorithms with fixed gains and nonstationary dependent data simulation results show the significant advantages of the tree structured piecewise linear filter over linear and polynomial filters for adaptive echo cancellation

convergence and performance analysis of the normalized lms algorithm with uncorrelated gaussian data it is demonstrated that the normalized least mean square nlms algorithm can be viewed as a modification of the widely used lms algorithm the nlms is shown to have an important advantage over the lms which is that its convergence is independent of environmental changes in addition the authors present a comprehensive study of the first and second order behavior in the nlms algorithm they show that the nlms algorithm exhibits significant improvement over the lms algorithm in convergence rate while its steady state performance is considerably worse

coupling of viscous and inviscid stokes equations via a domain decomposition method for finite elements a generalized stokes problem is addressed in the framework of a domain decomposition method in which the physical computational domain is partitioned into two subdomains 1 and 2 three different situations are covered in the former the viscous terms are kept in both subdomains then we consider the case in which viscosity is dropped out everywhere in finally a hybrid situation in which viscosity is dropped out only in 1 is addressed the latter is motivated by physical applications in all cases correct transmission conditions across the interface between 1 and 2 are devised and an iterative procedure involving the successive resolution of two subproblems is proposed the numerical discretization is based upon appropriate finite elements and stability and convergence analysis is carried out we also prove that the iteration by subdomain algorithms which are associated with the various domain decomposition approaches converge with a rate independent of the finite element mesh size

a variable step size lms algorithm a least mean square lms adaptive filter with a variable step size is introduced the step size increases or decreases as the mean square error increases or decreases allowing the adaptive filter to track changes in the system as well as produce a small steady state error the convergence and steady state behavior of the algorithm are analyzed the results reduce to well known results when specialized to the constant step size case simulation results are presented to support the analysis and to compare the performance of the algorithm with the usual lms algorithm and another variable step size algorithm they show that its performance compares favorably with these existing algorithms

a generalization of voiculescu s theorem for normal operators to semifinite von neumann algebras abstract in this paper we provide a generalized version of voiculescu s theorem for normal operators by showing that in a von neumann algebra with separable pre dual and a faithful normal semifinite tracial weight each normal operator is an arbitrarily small max 2 norm perturbation of a diagonal operator furthermore in a countably decomposable properly infinite von neumann algebra with a faithful normal semifinite tracial weight we prove that each self adjoint operator can be diagonalized modulo normed ideals satisfying a natural condition an analogue for nuclear c algebras of voiculescu s absorption theorem 33 theorem 2 4 is also proved in the case of semifinite factors

a variable step vs adaptive filter algorithm in recent work a new version of an lms algorithm has been developed which implements a variable feedback constant for each weight of an adaptive transversal filter this technique has been called the vs variable step algorithm and is an extension of earlier ideas in stochastic approximation for varying the step size in the method of steepest descents the method may be implemented in hardware with only modest increases in complexity approx 15 percent over the lms widrow hoff algorithm it is shown that an upper bound for the convergence time is the classical mean square error time constant and examples are given to demonstrate that for broad signal classes both narrow band and broad band the convergence time is reduced by a factor of up to 50 in noise canceller applications for the proper selection of variable step parameters finally the vs algorithm is applied to an iir filter and simulations are presented for applications of the vs fir and iir adaptive filters

a condition for diagonalization modulo arbitrary norm ideals abstract we give a spectral condition which is sufficient for the simultaneous diagonalization of a commuting tuple of self adjoint operators modulo a given norm ideal for diagonalization modulo certain norm ideals this condition is also necessary while for other norm ideals this condition seems to be close to being necessary moreover this condition is easy to verify in applications

linear regression and filtering under nonstandard assumptions arbitrary noise this note is devoted to parameter estimation in linear regression and filtering where the observation noise does not possess any nice probabilistic properties in particular the noise might have an unknown but bounded deterministic nature the basic assumption is that the model regressors inputs are random optimal rates of convergence for the modified stochastic approximation and least squares algorithms are established under some weak assumptions typical behavior of the algorithms in the presence of such deterministic noise is illustrated by numerical examples

gradient based variable forgetting factor rls algorithm in time varying environments in this paper a new control mechanism for the variable forgetting factor vff of the recursive least square rls adaptive algorithm is presented the control algorithm is basically a gradient based method of which the gradient is derived from an improved mean square error analysis of rls the new mean square error analysis exploits the correlation of the inverse of the correlation matrix with itself that yields improved theoretical results especially in the transient and steady state mean square error it is shown that the theoretical analysis is close to simulation results for different forgetting factors and different model orders the analysis yields a dynamic equation of mean square error that can be used to derive a dynamic equation of the gradient of mean square error to control the forgetting factor the dynamic equation can produce a positive gradient when the error is large and a negative gradient when the error is in the steady state compared with other variable forgetting factor algorithms the new control algorithm gives fast tracking and small mean square model error for different signal to noise ratios snrs

diagonalization modulo a class of orlicz ideals abstract we consider a class of norm ideals c g which are non commutative analogues of orlicz spaces and which satisfy a previously introduced condition called qk we give a spectral condition which is necessary and sufficient for a commuting tuple of self adjoint operators a a 1 a n to be simultaneously diagonalizable modulo c g

analysis of mean square error and transient speed of the lms adaptive algorithm for the least mean square lms algorithm we analyze the correlation matrix of the filter coefficient estimation error and the signal estimation error in the transient phase as well as in steady state we establish the convergence of the second order statistics as the number of iterations increases and we derive the exact asymptotic expressions for the mean square errors in particular the result for the excess signal estimation error gives conditions under which the lms algorithm outperforms the wiener filter with the same number of taps we also analyze a new measure of transient speed we do not assume a linear regression model the desired signal and the data process are allowed to be nonlinearly related the data is assumed to be an instantaneous transformation of a stationary markov process satisfying certain ergodic conditions

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

on statistical efficiency of the lms algorithm in system modeling the conventional least mean square lms algorithm is compared with the ideal lms newton ilmsn algorithm it is shown that although under certain conditions for similar misadjustment the output mean square error mse of the ilmsn algorithm may converge much faster than the mse of the lms algorithm the difference between the two algorithms may not be that great if misalignments of the adaptive filter tap gains are compared analytical results are presented with computer simulations that support their validity

necessary and sufficient conditions for stability of lms guo and ljung 1995 established some general results on exponential stability of random linear equations which can be applied directly to the performance analysis of a wide class of adaptive algorithms including the basic lms ones without requiring stationarity independency and boundedness assumptions of the system signals the current paper attempts to give a complete characterization of the exponential stability of the lms algorithms by providing a necessary and sufficient condition for such a stability in the case of possibly unbounded nonstationary and non spl phi mixing signals the results of this paper can be applied to a very large class of signals including those generated from e g a gaussian process via a time varying linear filter as an application several novel and extended results on convergence and the tracking performance of lms are derived under various assumptions neither stationarity nor markov chain assumptions are necessarily required in the paper

the stability of variable step size lms algorithms variable step site lms vslms algorithms are a popular approach to adaptive filtering which can provide improved performance while maintaining the simplicity and robustness of conventional fixed step size lms here we examine the stability of vslms with uncorrelated stationary gaussian data most vslms described in the literature use a data dependent step size where the step size either depends on the data before the current time prior step size rule or through the current time posterior step size rule it has often been assumed that vslms algorithms are stable in the sense of mean square bounded weights provided that the step size is constrained to lie within the corresponding stability region for the lms algorithm for a single tap fitter we find exact expressions for the stability region of vslms over the classes of prior and posterior step sizes and show that the stability region for prior step size coincides with that of fixed step size but the region for posterior step size is strictly smaller than for fixed step size for the multiple tap case we obtain bounds on the stability regions with similar properties the approach taken here is a generalization of the classical method of analyzing the exponential stability of the weight covariance equation for lms although it is not possible to derive a weight covariance equation for general data dependent vslms the weight variances can be upper bounded by the solution of a linear time invariant difference equation after appropriately dealing with certain nonlinear terms for prior step size like fixed step size the state matrix is symmetric whereas for posterior step size the symmetry is lost requiring a more detailed analysis the results are verified by computer simulations

adaptive stack filtering with application to image processing with the aid of threshold decomposition it is shown that optimal stack filters under the mean absolute error mae criterion are equal to optimal or bayesian classifiers subject to stacking constraints under the mean classification error mce criterion nonadaptive and adaptive constrained least mean absolute lma algorithms are developed for the esti mation of stack filters through the linearization of the unit step function in the objective function the convergence of the al gorithms is proven under certain conditions although the methods do not generally give optimal stack filters under the mae criterion these algorithms have several distinct merits compared to other stack filter optimization methods 1 the op timization problem has a unique solution that approximates the optimal stack filters in the least mean square sense 2 the meth ods can be implemented in the binary and real domains and 3 for stack filters defined by linearly separable positive boolean functions pbf s or weighted order statistic wos filters the number of the parameters to be estimated is reduced to the window width of the filter a comparison between images re stored by the new algorithms and the stack filtering algorithm optimal under the mae criterion confirms the effectiveness of the proposed algorithms

new substructuring domain decomposition methods for advection diffusion equations abstract in this paper we consider a nonsymmetric elliptic problem and we use the techniques related to the steklov poincare operators to propose new substructuring iterative procedures in particular we propose two methods that generalize the well known neumann neumann and dirichlet neumann iterative procedures we prove that our methods that use symmetric and positive definite preconditioners lead to the construction of iterative schemes with optimal convergence properties numerical results for the finite element discretization are given

convergence analysis of adaptive linear estimation for dependent stationary processes the convergence properties of an adaptive linear mean square estimator that uses a modified lms algorithm are established for generally dependent processes bounds on the mean square error of the estimates of the filter coefficients and on the excess error of the estimate of the signal are derived for input processes which are either strong mixing or asymptotically uncorrelated it is shown that the mean square deviation is bounded by a constant multiple of the adaptation step size and that the same holds for the excess error of the signal estimation the present findings extend earlier results in the literature obtained for independent and m dependent input data

second order convergence analysis of stochastic adaptive linear filtering the convergence of an adaptive filtering vector is studied when it is governed by the mean square error gradient algorithm with constant step size we consider the mean square deviation between the optimal filter and the actual one during the steady state this quantity is known to be essentially proportional to the step size of the algorithm however previous analyses were either heuristic or based upon the assumption that successive observations were independent which is far from being realistic actually in most applications two successive observation vectors share a large number of components and thus they are strongly correlated in this work we deal with the case of correlated observations and prove that the mean square deviation is actually of the same order or less than the step size of the algorithm this result is proved without any boundedness or barrier assumption for the algorithm as it has been done previously in the literature to ensure the nondivergence our assumptions are reduced to the finite strong memory assumption and the finite moments assumption for the observation they are satisfied in a very wide class of practical applications

convergence in distribution of lms type adaptive parameter estimates we study the asymptotic behavior of parameter estimates generated by lms least mean square adaptive estimation algorithms in stationary dependent random situations we show that subject to mild practically reasonable conditions the estimates converge in distribution further we extend this result to prove a more explicit type of convergence in distribution which explains other observed properties we then estimate the moments of this limiting distribution and discuss how this relates to the work of others

stochastic stability analysis for the constant modulus algorithm we derive an easy to compute approximate bound for the range of step sizes for which the constant modulus algorithm cma will remain stable if initialized close to a minimum of the cm cost function our model highlights the influence of the signal constellation used in the transmission system for smaller variation in the modulus of the transmitted symbols the algorithm will be more robust and the steady state misadjustment will be smaller the theoretical results are validated through several simulations for long and short filters and channels

splitting methods based on algebraic factorization for fluid structure interaction we discuss in this paper the numerical approximation of fluid structure interaction fsi problems dealing with strong added mass effect we propose new semi implicit algorithms based on inexact block lu factorization of the linear system obtained after the space time discretization and linearization of the fsi problem as a result the fluid velocity is computed separately from the coupled pressure structure velocity system at each iteration reducing the computational cost we investigate explicit implicit decomposition through algebraic splitting techniques originally designed for the fsi problem this approach leads to two different families of methods which extend to fsi the algebraic pressure correction method and the yosida method two schemes that were previously adopted for pure fluid problems furthermore we have considered the inexact factorization of the fluid structure system as a preconditioner the numerical properties of these methods have been tested on a model problem representing a blood vessel system

performance analysis of the deficient length lms adaptive algorithm in almost all analyzes of the least mean square lms finite impulse response fir adaptive algorithm it is assumed that the length of the adaptive filter is equal to that of the unknown system impulse response however in many practical situations a deficient length adaptive filter whose length is less than that of the unknown system is employed and analysis results for the sufficient length lms algorithm are not necessarily applicable to the deficient length case therefore there is an essential need to accurately quantify the behavior of the lms algorithm for realistic situations where the length of the adaptive filter is deficient in this paper we present a performance analysis for the deficient length lms adaptive algorithm for correlated gaussian input data and using the common independence assumption exact expressions that completely characterize the transient and steady state mean square performances of the algorithm are developed which lead to new insights into the statistical behavior of the deficient length lms algorithm simulation experiments illustrate the accuracy of the theoretical results in predicting the convergence behavior of the algorithm

a robust recursive least squares algorithm a new algorithm is developed which guarantees the normalized bias in the weight vector due to persistent and bounded data perturbations to be bounded robustness analysis for this algorithm has been presented an approximate recursive implementation is also proposed it is termed as the robust recursive least squares rrls algorithm since it resembles the rls algorithm in its structure and is robust with respect to persistent bounded data perturbation simulation results are presented to illustrate the efficacy of the rrls algorithm

convergence of an adaptive linear estimation algorithm in this work we prove the almost sure convergence of an adaptive linear estimator governed by a stochastic gradient algorithm with decreasing step size in the presence of correlated observations two complementary contributions are added to the famous 1977 ljung theorem first we drop the condition of nondivergence of the algorithm assumed by ljung while that condition can be ensured by adding a barrier the convergence of the suitably bounded algorithm itself is not established even on the basis of ljung theorem here the barrier problem is overcome by proving that it is not necessary for the convergence our second contribution is to generalize the model describing the correlated observations no state space model is used and no linear relationship between the observations and the signal to be estimated needs to be assumed instead we use a decreasing covariance model that agrees with a very wide class of practical applications

convergence analysis of lms filters with uncorrelated gaussian data statistical analysis of the least mean squares lms adaptive algorithm with uncorrelated gaussian data is presented exact analytical expressions for the steady state mean square error mse and the performance degradation due to weight vector misadjustment are derived necessary and sufficient conditions for the convergence of the algorithm to the optimal wiener solution within a finite variance are derived it is found that the adaptive coefficient which controls the rate of convergence of the algorithm must be restricted to an interval significantly smaller than the domain commonly stated in the literature the outcome of this paper therefore places fundamental limitations on the mse performance and rate of convergence of the lms adaptive scheme

a stochastic gradient adaptive filter with gradient adaptive step size the step size of this adaptive filter is changed according to a gradient descent algorithm designed to reduce the squared estimation error during each iteration an approximate analysis of the performance of the adaptive filter when its inputs are zero mean white and gaussian noise and the set of optimal coefficients are time varying according to a random walk model is presented the algorithm has very good convergence speed and low steady state misadjustment the tracking performance of these algorithms in nonstationary environments is relatively insensitive to the choice of the parameters of the adaptive filter and is very close to the best possible performance of the least mean square lms algorithm for a large range of values of the step size of the adaptation algorithm several simulation examples demonstrating the good properties of the adaptive filters as well as verifying the analytical results are also presented

diagonalization modulo norm ideals with lipschitz estimates abstract suppose that x d is a compact metric space and that is a regular borel measure on x let lip x denote the collection of lipschitz functions on x in this paper we investigate the problem of simultaneous diagonalization of the multiplication operators m f f lip x on l 2 x modulo norm ideals of compact operators

numerical solution of the elastic body plate problem by nonoverlapping domain decomposition type techniques the purpose of this paper is to provide two numerical methods for solving the elastic body plate problem by nonoverlapping domain decomposition type techniques based on the discretization method by wang the first one is similar to an older method but here the corresponding schur complement matrix is preconditioned by a specific preconditioner associated with the plate problem the second one is a displacement force type schwarz alternating method at each iteration step of the two methods either a pure body or a pure plate problem needs to be solved it is shown that both methods have a convergence rate independent of the size of the finite element mesh

transient analysis of data normalized adaptive filters this paper develops an approach to the transient analysis of adaptive filters with data normalization among other results the derivation characterizes the transient behavior of such filters in terms of a linear time invariant state space model the stability of the model then translates into the mean square stability of the adaptive filters likewise the steady state operation of the model provides information about the mean square deviation and mean square error performance of the filters in addition to deriving earlier results in a unified manner the approach leads to stability and performance results without restricting the regression data to being gaussian or white the framework is based on energy conservation arguments and does not require an explicit recursion for the covariance matrix of the weight error vector

recursive nonlinear system identification by a stochastic gradient algorithm stability performance and model nonlinearity considerations a parameter estimation problem in a class of nonlinear systems is considered where the input output relation of a nonlinear system is approximated by a polynomial model e g a volterra series a least mean squares lms type algorithm is utilized for the recursive estimation of the polynomial coefficients and its resulting mean square error mse convergence properties are investigated conditions for the algorithm stability in the mean square sense are established steady state mse bounds are obtained and the convergence rate is discussed in addition modeling accuracy versus steady state performance is examined it is found that an increase of the modeling accuracy may result in a deterioration of the asymptotic performance that is yielding a larger steady state mse linear system identification is studied as a special case

convergence analysis of domain decomposition algorithms with full overlapping for the advection diffusion problems the aim of this paper is to study the convergence properties of a time marching algorithm solving advection diffusion problems on two domains using incompatible discretizations the basic algorithm is first presented and theoretical or numerical results illustrate its convergence properties this study is based on spectral theory a priori estimates and a di giorgi nash maximum principle

analysis and implementation of variable step size adaptive algorithms stochastic gradient adaptive filtering algorithms using variable step sizes are investigated the variable step size algorithm improves the convergence rate while sacrificing little in steady state error expressions describing the convergence of the mean and mean squared values of the coefficients are developed and used to calculate the mean square error evolution the initial convergence rate and the steady state error are also investigated the performance of the algorithm is studied when a power of two quantizer algorithm is used and finite word length effects are considered the analytical results are verified with simulations encompassing variable applications two cmos implementations of the variable step size power of two quantizer algorithm are presented to demonstrate that the performance gains are attainable with only a modest increase in circuit complexity

analysis of adaptive step size sa algorithms for parameter tracking we present proofs and data for adaptive step size algorithms for tracking time varying parameters when recursive stochastic approximation type algorithms are used a classical problem in adaptive control and communication theory concerns the tracking of the best fit of a given form when the statistics or the parameters change slowly a major and yet unresolved problem has been the choice of the step sizes in the tracking algorithm an algorithm for adapting the step size using the same system measurements which are used for the tracking was suggested by benveniste and various examples worked out by brossier the numerical results were very encouraging but proofs were lacking these proofs are supplied here together with supporting numerical data the proofs are based on recent results in stochastic approximation the adaptive step size technique works very well indeed much supporting analysis is presented particularly concerning the interpretation of certain stationary processes as stationary pathwise derivatives finite difference forms are also treated these are mathematically simpler and can be applied to a wide variety of systems even when the system is not well modeled the data shows that they work well

constrained adaptive filtering algorithms asymptotic convergence properties for dependent data the convergence properties of constrained adaptive filtering algorithms are established the constraint is in the form of a bounded set in which the filter s coefficients must lie a recursive procedure that converges to the deterministic solution of the constrained linear mean square estimation problem is obtained using an appropriate contraction mapping the recursion is used to derive the adaptive algorithm for the filter coefficients bounds on the mean square error of the coefficients bounds on the mean square error of the estimates of the filter coefficients and on the excess error of the input signal estimate are derived for processes that are either strong mixing or asymptotically uncorrelated the algorithms use a moving window of size n on the data from one adaptation step to the next however tighter bounds can be obtained when a skipped sampling mechanism is used

an optimal domain decomposition preconditioner for low frequency time harmonic maxwell equations the time harmonic maxwell equations are considered in the low frequency case a finite element domain decomposition approach is proposed for the numerical approximation of the exact solution this leads to an iteration by subdomain procedure which is proven to converge the rate of convergence turns out to be independent of the mesh size showing that the preconditioner implicitly defined by the iterative procedure is optimal for obtaining this convergence result it has been necessary to prove a regularity theorem for dirichlet and neumann harmonic fields

singular integral operators and norm ideals satisfying a quantitative variant of kuroda s condition a norm ideal c is said to satisfy condition qk if there exist constants 0 t 1 and 0 b such that x k c bkt x c for every finite rank operator x and every k n where x k denotes the direct sum of k copies of x let be a regular borel measure whose support is contained in a unit cube q in rn and let kj be the singular integral operator on l2 rn with the kernel function xj yj x y 2 1 j n let qw w w be the usual dyadic decomposition of q i e qw w l is the dyadic partition of q by cubes of the size 2 l 2 l we show that if c satisfies qk and if w w2 w qw w w c where c is the dual of c 0 and w w w is any orthonormal set then k1 kn c this is a very general obstruction result for the problem of simultaneous diagonalization of commuting tuples of self adjoint operators modulo c

a robust variable step size lms type algorithm analysis and simulations a number of time varying step size algorithms have been proposed to enhance the performance of the conventional lms algorithm experimentation with these algorithms indicates that their performance is highly sensitive to the noise disturbance this paper presents a robust variable step size lms type algorithm providing fast convergence at early stages of adaptation while ensuring small final misadjustment the performance of the algorithm is not affected by existing uncorrelated noise disturbances an approximate analysis of convergence and steady state performance for zero mean stationary gaussian inputs and for nonstationary optimal weight vector is provided simulation results comparing the proposed algorithm to current variable step size algorithms clearly indicate its superior performance for cases of stationary environments for nonstationary environments our algorithm performs as well as other variable step size algorithms in providing performance equivalent to that of the regular lms algorithm

noise constrained least mean squares algorithm we consider the design of an adaptive algorithm for finite impulse response channel estimation which incorporates partial knowledge of the channel specifically the additive noise variance although the noise variance is not required for the offline wiener solution there are potential benefits and limitations for the learning behavior of an adaptive solution in our approach a robbins monro algorithm is used to minimize the conventional mean square error criterion subject to a noise variance constraint and a penalty term necessary to guarantee uniqueness of the combined weight multiplier solution the resulting noise constrained lms nclms algorithm is a type of variable step size lms algorithm where the step size rule arises naturally from the constraints a convergence and performance analysis is carried out and extensive simulations are conducted that compare nclms with several adaptive algorithms this work also provides an appropriate framework for the derivation and analysis of other adaptive algorithms that incorporate partial knowledge of the channel

a domain decomposition approach for heterogeneous time harmonic maxwell equations the time harmonic maxwell equations for a composite medium which behaves like a conductor in one part and like a perfect insulator in the other one are considered an existence and uniqueness theorem is proven for this degenerate problem in the case of dirichlet boundary conditions a finite element domain decomposition approach is then proposed for the numerical approximation of the exact solution this leads to an iteration by subdomain procedure where at each step a non degenerate boundary value problem has to be solved in each subdomain the convergence of these iterations is proven and the rate of convergence turns out to be independent of the mesh size h showing that the preconditioner implicitly defined by the iteration procedure is optimal

adaptive enhancement of finite bandwidth signals in white gaussian noise the steady state behavior of the adaptive line enhancer ale is analyzed for stationary inputs consisting of finite bandwidth signals embedded in a white gaussian noise wgn background analytic expressions for the weights and output of the lms adaptive filter are derived as functions of input signal bandwidth and snr as well as ale length and bulk delay the steady state gain in broad band snr from input to output is derived as a function of these same four variables for fixed ale parameters and input snr it is shown that this gain increases as the input signal becomes narrower and approaches the sinusoidal limit it is emphasized that because the correlation time of finite bandwidth signals is limited excessively large values of the ale bulk delay parameter result in diminished gain furthermore there is an optimal filter length whose value depends upon signal bandwidth and snr for which the broad band gain is maximized these results demonstrate the importance of including the effects of algorithm noise in analyzing the performance of real time adaptive processors

the 2r th mean convergence of adaptive filters with stationary dependent random variables the 2r th mean convergence of an adaptive filtering algorithm c n 1 c n a n c n t x n alpha n x n is studied where alpha n s and x n s are useful random signals and observation vectors respectively and a n is a sequence of positive numbers decreasing to zero in this work we suppose that the sequence alpha n x n is a stationary mixing sequence rho mixing phi mixing or psi mixing under some additional conditions it is shown that c n converges to c ast in the 2r th mean where c ast is the unique solution of the wiener hopf equation

asymptotic behavior of an adaptive estimation algorithm with application to m dependent data theoretical results are presented concerning the asymptotic behavior of the parameter estimates generated by an adaptive algorithm in stationary dependent random situations proofs are exhibited in the general case and derived for the case of statistical dependence in the input for a finite number of lags it is found that the estimate mean error norm converges to an asymptotic bound giving a finite bias generally nonzero and that the asymptotic mean norm square error is bounded and can be arbitrarily reduced by decreasing the adaptation factor

diagonalization and unitary equivalence modulo schatten p classes we give a necessary and sufficient condition for a commuting tuple a a1 an of self adjoint operators to be simultaneously diagonalizable modulo cp 1 p

convergence rate determined for gradient based adaptive estimators abstract a convergence rate estimate is derived for the homogeneous gradient based adaptive linear estimator algorithm this estimate involves the eigenvalues of the regression vector covariance matrix yielding a useful measure for the choice of input signals for adaptive parameter estimation the connection between this criterion and those more familiar from nonadaptive system identification is made and comparisons are drawn between the two areas