a fast algorithm for apes and capon spectral estimation in this paper we derive a novel implementation of some very computationally demanding matched filter bank based spectral estimators namely the amplitude and phase estimator apes the amplitude spectrum capon asc estimator and the power spectrum capon psc estimator filter bank based spectral estimation methods that adopt data dependent filter banks can provide spectra characterized by a significantly improved resolution compared to classical approaches however the computational complexity of the currently available implementation algorithms is extremely high a novel technique is introduced that provides efficient algorithms for the computation of the apes asc and psc spectra the proposed method is based on suitable displacement representations of all pertinent data matrices that are subsequently utilized for the computation of the associated complex valued polynomials the computational complexity of the proposed algorithms is lower than all relevant existing methods

a finite element method for the simulation of strong and weak discontinuities in solid mechanics in this paper we introduce and analyze a finite element method for elasticity problems with interfaces the method allows for discontinuities internal to the elements in the approximation across the interface we propose a general approach that can handle both perfectly and imperfectly bonded interfaces without modifications of the code for the case of linear elasticity we show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh we present numerical examples for the linear case as well as for contact and crack propagation model problems

structure generating mechanisms in agent based models abstract the emergence of dynamical structures in multi agent systems is analysed three different mechanisms are identified namely 1 sensitive dependence in the agent dynamics and convex coupling 2 sensitive dependence and extremal dynamics and 3 interaction through a collectively generated field the dynamical origin of the emergent structures is traced back either to a modification by interaction of the lyapunov spectrum or to multistable dynamics

displacement structure for hankel vandermonde and related derived matrices abstract we introduce some generalized concepts of displacement structure for structured matrices obtained as products and inverses of toeplitz hankel and vandermonde matrices the toeplitz case has already been studied at some length and the corresponding matrices have been called near toeplitz or toeplitz like or toeplitz derived we focus on hankel and vandermonde like matrices and in particular show how the appropriately defined displacement structure yields fast triangular and orthogonal factorization algorithms for such matrices the main contribution of this paper is presenting a unified framework rather than obtaining the fastest algorithm for each special matrix

extended chandrasekhar recursions we extend the discrete time chandrasekhar recursions for least squares estimation in constant parameter state space models to a class of structured time variant state space models special cases of which often arise in adaptive filtering it can be shown that the much studied exponentially weighted recursive least squares filtering problem can be reformulated as an estimation problem for a state space model having this special time variant structure other applications arise in the multichannel and multidimensional adaptive filtering context

the spectral approximation of multiplication operators via asymptotic structured linear algebra abstract a multiplication operator on a hilbert space may be approximated with finite sections by choosing an orthonormal basis of the hilbert space multiplication operators with nonzero symbols defined on l 2 spaces of functions are never compact and then such approximations cannot converge in the norm topology instead we consider how well the spectra of the finite sections approximate the spectrum of the multiplication operator whose expression is simply given by the essential range of the symbol i e the multiplier we discuss the case of real orthogonal polynomial bases and the relations with the classical fourier basis whose choice leads to the well studied toeplitz case indeed the asymptotic approximation of the spectrum by the spectra of the associated toeplitz sections is possible only under precise geometric assumptions on the range of the symbol conversely the use of circulant approximations leads to constructive algorithms with o n log n complexity n number of sections working in general and generalizable to the separable multivariate and matrix valued cases as well

on the solution of the minimal rational interpolation problem it is shown that the reachability and the observability indices of appropriately defined pairs of matrices provide the key for solving the minimal rational bitangen tial interpolation problem

simple deterministic self organized critical system we introduce a continuous cellular automaton that presents self organized criticality it is one dimensional totally deterministic without any embedded randomness not even in the initial conditions this system is in the same universality class as the oslo rice pile boundary driven interface depinning and the train model for earthquakes although the system is chaotic in the thermodynamic limit chaos occurs only in a microscopic level

an immersed discontinuous finite element method for stokes interface problems abstract we present a discontinuous immersed finite element ife method for stokes interface problems on cartesian meshes that do not require the mesh to be aligned with the interface as such the method allows unfitted meshes with elements cut by the interface and thus may contain more than one fluid on these unfitted meshes we construct an immersed q 1 q 0 finite element space according to the location of the interface and pertinent interface jump conditions the proposed q 1 q 0 ife shape functions have several desirable features such as the unisolvence and the partition of unity we present several numerical examples to demonstrate that the proposed ife spaces maintain the optimal approximation capability with respect to the polynomials used we also show that related discontinuous ife solutions of stokes interface problems maintain the optimal convergence rates in both l 2 and broken h 1 norms

a look ahead levinson algorithm for general toeplitz systems the authors present an extension of levinson s algorithm that is guaranteed to be weakly stable for a large class of general toeplitz matrices namely those that do not have many consecutive ill conditioned leading principal submatrices the new algorithm adapts itself to the given toeplitz matrix by skipping over all the ill conditioned leading principal submatrices encountered during the solution process this is done by a look ahead strategy that monitors the condition of the leading principal submatrices and if necessary switches to a block step of suitable size the overhead of the look ahead algorithm is typically small compared to the classical levinson algorithm and in addition a reliable condition number estimate is produced

power spectrum of mass and activity fluctuations in a sandpile we consider a directed abelian sandpile on a strip of size 2 ifmmode times else texttimes fi n driven by adding a grain randomly at the left boundary after every t timesteps we establish the exact equivalence of the problem of mass fluctuations in the steady state and the number of zeros in the ternary base representation of the position of a random walker on a ring of size 3 n we find that while the fluctuations of mass have a power spectrum that varies as 1 f for frequencies in the range 3 ensuremath 2n ensuremath ll f ensuremath ll 1 t the activity fluctuations in the same frequency range have a power spectrum that is linear in f

hankel and loewner matrices abstract mutual relations between the hankel toeplitz bezout and loewner matrices as well as further connections to rational interpolation and projective geometry are investigated

an unfitted finite element method based on nitsche s method for elliptic interface problems in this paper we propose a method for the finite element solution of elliptic interface problem using an approach due to nitsche the method allows for discontinuities internal to the elements in the approximation across the interface we show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh further we derive a posteriori error estimates for the purpose of controlling functionals of the error and present some numerical examples

a conforming enriched finite element method for stokes interface problems abstract a new conforming enriched finite element method is presented for stokes interface problems with interface unfitted meshes the conforming enriched finite element pair is constructed based on the mini element pair a ghost penalty term is used in the standard discretization form as a stabilization term an inf sup stability result is derived which is uniform with respect to the mesh size our method does not limit the viscosity coefficient to be a piecewise constant finite element errors are proved to be optimal numerical experiments are carried out to validate theoretical results

new cartesian grid methods for interface problems using the finite element formulation new finite element methods based on cartesian triangulations are presented for two dimensional elliptic interface problems involving discontinuities in the coefficients the triangulations in these methods do not need to fit the interfaces the basis functions in these methods are constructed to satisfy the interface jump conditions either exactly or approximately both non conforming and conforming finite element spaces are considered corresponding interpolation functions are proved to be second order accurate in the maximum norm the conforming finite element method has been shown to be convergent with cartesian triangulations these new methods can be used as finite difference methods numerical examples are provided to support the methods and the theoretical analysis

the extended generalized finite element method an overview of the method and its applications an overview of the extended generalized finite element method gefm xfem with emphasis on methodological issues is presented this method enables the accurate approximation of solutions that involve jumps kinks singularities and other locally non smooth features within elements this is achieved by enriching the polynomial approximation space of the classical finite element method the gefm xfem has shown its potential in a variety of applications that involve non smooth solutions near interfaces among them are the simulation of cracks shear bands dislocations solidification and multi field problems copyright 2010 john wiley sons ltd

fast recursive identification of state space models via exploitation of displacement structure abstract the seemingly computational burden of state space model identification has limited its real time application though it offers some important advantages over methods based on input output transfer functions it has been shown recently that ideas from the theory of displacement structure can be used in state space identification to reduce the computational burden of batch processing from o mn 2 to o mn flops when the data matrix is of size m n where n m however in many on line identification scenarios with slowly time varying systems it is desirable to update the model as time goes on with the minimal computational burden in this paper we extend our results of the batch processing algorithm to allow updating of the identified state space model with o m 2 flops again the theories of displacement structure and of the fast subspace decomposition fsd technique play crucial roles in the realization of the fast updating algorithm some computer simulation results are also presented

hyperbolic householder transformations a class of transformation matrices analogous to the householder matrices is developed with a nonorthogonal property designed to permit the efficient deletion of data from least squares problems these matrices which we term hyperbolic householder are shown to effect deletion or simultaneous addition and deletion of data with much less sensitivity to rounding errors than for techniques based on normal equations when the addition deletion sets are large this numerical robustness is obtained at the expense of only a modest increase in computations and when only a relatively small fraction of the data set is modified there is a decrease in required computations two applications to signal processing problems are considered first these transformations are used to obtain a square root algorithm for windowed recursive least squares filtering second the transformations are employed to implement the rejection of spurious data from the weight vector estimator in an adaptive array

an interpolation theory approach to h controller degree bounds abstract we derive upper bounds for the mcmillan degree of all h optimal controllers associated with design problems which may be embedded in a certain generalized regular configuration our analysis is confined to problems of the first kind which are characterized by the assumption that both p12 s and p21 s are square but not necessarily of the same size this paper which uses interpolation theory complements a previous paper which addresses the same problem through an approach based on approximation theory we demonstrate that the interpolation theory approach is more direct and circumvents a number of the technical difficulties in the previous method the final outcome is a much shorter proof as a by product we achieve a new result on the degree of an optimal solution of the matrix nevanlinna pick problem

partially penalized immersed finite element methods for elliptic interface problems this article presents new immersed finite element ife methods for solving the popular second order elliptic interface problems on structured cartesian meshes even if the involved interfaces have nontrivial geometries these ife methods contain extra stabilization terms introduced only at interface edges for penalizing the discontinuity in ife functions with the enhanced stability due to the added penalty not only can these ife methods be proven to have the optimal convergence rate in an energy norm provided that the exact solution has sufficient regularity but also numerical results indicate that their convergence rates in both the h 1 norm and the l 2 norm do not deteriorate when the mesh becomes finer which is a shortcoming of the classic ife methods in some situations trace inequalities are established for both linear and bilinear ife functions that are not only critical for the error analysis of these new ife methods but are also of a great potential to be useful in error analysis for other

superfast approximative implementation of the iaa spectral estimate in this correspondence we develop superfast approximative one dimensional algorithms for the computationally efficient implementation of the recent iterative adaptive approach iaa spectral estimate the proposed methods are based on rewriting the iaa algorithm with suitable gohberg semencul representations solving the resulting linear systems of equations using the preconditioned conjugate gradient method where a novel preconditioning is applied using an incomplete factorization of the toeplitz matrix numerical simulations illustrate the efficiency of both the proposed preconditioning as well as the overall algorithm offering a computational reduction of up to two orders of magnitude as compared to our recently proposed efficient and exact iaa implementation

fast matrix factorizations via discrete transmission lines abstract fast algorithms associated with the names of schur and levinson are known for the triangular factorization of symmetric positive definite toeplitz matrices and their inverses in this paper we show that these algorithms can be derived from simple arguments involving causality symmetry and energy conservation in discrete lossless transmission lines the results not only provide a nice interpretation of the classical schur and levinson algorithms and a certain toeplitz inversion formula of gohberg and semencul but they also show immediately that the same fast algorithms apply not only to toeplitz matrices but to all matrices with so called displacement inertia 1 1 the results have been helpful in suggesting new digital filter structures and in the study of nonstationary second order processes

the one dimensional inverse problem of reflection seismology an impulsive normal traction is applied uniformly over the surface of a perfectly stratified plane layered earth the ensuing particle velocity at the surface is assumed to be measured the problem of calculating the subsurface characteristic impedance from knowledge of the input pulse and the measured data is the one dimensional inverse problem of reflection seismology the problem is set up mathematically as an inverse problem for a first order 2 times 2 hyperbolic system the role of propagation of singularities is explained and the relation between the solution of the inverse problem and the cholesky factorization of certain matrices constructed from the data is elaborated for both the continuum problem and the related discrete problem it is found that recursive numerical techniques such as the levinson algorithm and certain other fast methods for cholesky factorization are intimately related to explicit finite difference schemes for solving hyperbolic systems the order of approximation between the

stabilized hyperbolic householder transformations a modification of the hyperbolic householder scheme is introduced which is demonstrably stable theoretically according to an established stability criterion and which exhibits superior numerical behavior in simulations the modified transform scheme effects downdating by applying conventional orthonormal rather than hyperbolic householder transformations to the data the latter have preferable numerical properties however the construction of these orthonormal operators itself requires hyperbolic computations thus the proposed method is in some sense half hyperbolic and half orthonormal there is no computational penalty incurred with these stabilized hyperbolic householder transforms they enjoy an operation count identical to their conventional counterparts

a new frequency estimation method for equally and unequally spaced data spectral estimation is an important classical problem that has received considerable attention in the signal processing literature in this contribution we propose a novel method for estimating the parameters of sums of complex exponentials embedded in additive noise from regularly or irregularly spaced samples the method relies on kronecker s theorem for hankel operators which enables us to formulate the nonlinear least squares problem associated with the spectral estimation problem in terms of a rank constraint on an appropriate hankel matrix this matrix is generated by sequences approximating the underlying sum of complex exponentials unequally spaced sampling is accounted for through a proper choice of interpolation matrices the resulting optimization problem is then cast in a form that is suitable for using the alternating direction method of multipliers admm the method can easily include either a nuclear norm or a finite rank constraint for limiting the number of complex exponentials the usage of a finite rank constraint makes in contrast to the nuclear norm constraint the method heuristic in the sense that the problem is non convex and convergence to a global minimum can not be guaranteed however we provide a large set of numerical experiments that indicate that usage of the finite rank constraint nevertheless makes the method converge to minima close to the global minimum for reasonably high signal to noise ratios hence essentially yielding maximum likelihood parameter estimates moreover the method does not seem to be particularly sensitive to initialization and performs substantially better than standard subspace based methods

fast gaussian elimination with partial pivoting for matrices with displacement structure fast o n 2 implementation of gaussian elimination with partial pivoting is designed for matrices possessing cauchy like displacement structure we show how toeplitz like toeplitz plus hankel like and vandermonde like matrices can be transformed into cauchy like matrices by using discrete fourier cosine or sine transform matrices in particular this allows us to propose a new fast o n 2 toeplitz solver gko which incorporates partial pivoting a large set of numerical examples showed that gko demonstrated stable numerical behavior and can be recommended for solving linear systems especially with nonsymmetric indefinite and ill conditioned positive definite toeplitz matrices it is also useful for block toeplitz and mosaic toeplitz toeplitz block matrices the algorithms proposed in this paper suggest an attractive alternative to look ahead approaches where one has to jump over ill conditioned leading submatrices which in the worst case requires o n 3 operations

remarks on the origin of the displacement rank concept an account is given of how a relationship was found between some equations of chandrasekhar for solving the wiener hopf integral equations and the nonlinear riccati differential equations encountered in linear least squares estimation problems for systems described in state space form a paper by casti kalaba and murthy 1972 provided the inspiration for seeking such a relationship and then extending it and applying it in many other fields using the concept of displacement structure

approximate inverse free preconditioners for toeplitz matrices abstract in this paper we propose approximate inverse free preconditioners for solving toeplitz systems the preconditioners are constructed based on the famous gohberg semencul formula we show that if a toeplitz matrix is generated by a positive bounded function and its entries enjoys the off diagonal decay property then the eigenvalues of the preconditioned matrix are clustered around one experimental results show that the proposed preconditioners are superior to other existing preconditioners in the literature

on drazin inverse of singular toeplitz matrix in this paper we show that the drazin inverse of singular toeplitz matrix can be represented as a sum of products of lower and upper triangular toeplitz matrices and give the explicit expression which generalizes the well known result by gohberg and semencul regarding the inverse of toeplitz matrix

an analysis of a broken p_1 nonconforming finite element method for interface problems we study some numerical methods for solving a second order elliptic problem with interface we introduce an immersed finite element method based on the broken p 1 nonconforming piecewise linear polynomials on interface triangular elements having edge averages as degrees of freedom these linear polynomials are broken to match the homogeneous jump condition along the interface which is allowed to cut through the element we prove optimal orders of convergence in the h 1 and l 2 norm next we propose a mixed finite volume method in the context introduced in s h chou d y kwak and k y kim math comp 72 2003 pp 525 539 using the raviart thomas mixed finite element and this broken p 1 nonconforming element the advantage of this mixed finite volume method is that once we solve the symmetric positive definite pressure equation without lagrangian multiplier the velocity can be computed locally by a simple formula this procedure avoids solving the saddle point problem furthermore we show optimal error estimates of velocity and pressure in our mixed finite volume method numerical results show optimal orders of error in the l 2 norm and broken h 1 norm for the pressure and in the h mathrm div norm for the velocity

analysis of an xfem discretization for stokes interface problems we consider a stationary stokes interface problem in the discretization the interface is not aligned with the triangulation for the discretization we use the p 1 extended finite element space p 1 xfem for the pressure and the standard conforming p 2 finite element space for the velocity since this pair is not necessarily lbb stable a consistent stabilization term known from the literature is added for the discrete bilinear form an inf sup stability result is derived which is uniform with respect to h mesh size parameter the viscosity quotient mu 1 mu 2 and the position of the interface in the triangulation based on this discretization error bounds are derived an optimal preconditioner for the stiffness matrix corresponding to this pair p 1 xfe for pressure and p 2 fe for velocity is presented the preconditioner has block diagonal form with a multigrid preconditioner for the velocity block and a new schur complement preconditioner optimality of this block preconditioner

inverse scattering for discrete transmission line models this paper presents several methods for the identification of the impedance and reflection coefficient profile of a nonuniform discrete transmission line from its response to a given forcing function this problem is the prototype for a wealth of one dimensional inverse scattering problems arising in various fields a unified straightforward approach is presented providing all known inversion procedures and some novel ones the derivations readily follow from causality of signal propagation on the transmission line it is shown that a direct exploitation of the signal propagation model leads to recursive computationally efficient and reliable inversion algorithms in particular the relationships between layer peeling schur type difference equation and layer adjoining levinson type integral equation algorithms are clearly displayed

fast newton transversal filters a new class of adaptive estimation algorithms a class of adaptive algorithms for the estimation of fir finite impulse response transversal filters is presented the main characteristic of this class is the fast computation of the gain vector needed for the adaptation of the transversal filters the method for deriving these algorithms is based on the assumption that the input signal is autoregressive of order m where m can be much smaller than the order of the filter to be estimated under this assumption the covariance matrix of the input signal is estimated by extending in a min max way the m order sample covariance matrix this estimate can be regarded as a generalization of the diagonal covariance matrix used in lms and leads to an efficient computation of the gain needed for the adaptation the new class of algorithms contains the lms and the fast versions of ls as special cases the complexity changes linearly with m starting from the complexity of the lms for m 0 and ending at the complexity of the fast versions of ls

a schur algorithm and linearly connected processor array for toeplitz plus hankel matrices a levinson durbin type algorithm for solving toeplitz plus hankel t h linear systems of equations is used to induce a schur type algorithm for such systems a schur type algorithm is defined as one which efficiently computes the ldu decomposition of the matrix on the other hand levinson durbin type algorithms are defined as those algorithms which efficiently compute the udl decomposition of the inverse of a matrix it is shown that the schur algorithm so obtained is amenable to efficient implementation on a linearly connected array of processors in a manner which generalizes the results of s y kung and y h ku 1983 for symmetric toeplitz matrices specifically if t h is of order n then the schur algorithm runs on o n processors in o n time

a look ahead bareiss algorithm for general toeplitz matrices the bareiss algorithm is one of the classical fast solvers for systems of linear equations with toeplitz coefficient matrices the method takes advantage of the special structure and it computes the solution of a toeplitz system of order n with only o n 2 arithmetic operations instead of o n 3 operations however the original bareiss algorithm requires that all leading principal submatrices be nonsingular and the algorithm is numerically unstable if singular or ill conditioned submatrices occur in this paper an extension of the bareiss algorithm to general toeplitz systems is presented using look ahead techniques the proposed algorithm can skip over arbitrary blocks of singular or ill conditioned submatrices and at the same time it still fully exploits the toeplitz structure implementation details and operations counts are given and numerical experiments are reported we also discuss special versions of the proposed look ahead bareiss algorithm for hermitian indefinite toeplitz systems and banded toeplitz systems

the hyberbolic singular value decomposition and applications a new generalization of the singular value decomposition svd the hyperbolic svd is advanced and its existence is established under mild restrictions the hyperbolic svd accurately and efficiently finds the eigenstructure of any matrix that is expressed as the difference of two matrix outer products signal processing applications where this task arises include the covariance differencing algorithm for bearing estimation in sensor arrays sliding rectangular windowing and array calibration two algorithms for effecting this decomposition are detailed one is sequential and follows a similar pattern to the sequential bidiagonal based svd algorithm the other is for parallel implementation and mimics hestenes svd algorithm 1958 numerical examples demonstrate that like its conventional counterpart the hyperbolic svd exhibits superior numerical behavior relative to explicit formation and solution of the normal equations furthermore the hyperbolic svd applies in problems where the conventional svd cannot be employed

efficient implementation of iterative adaptive approach spectral estimation techniques this paper presents computationally efficient implementations for several recent algorithms based on the iterative adaptive approach iaa for uniformly sampled one and two dimensional data sets considering both the complete data case and the cases when the data sets are missing samples either lacking arbitrary locations or having gaps or periodically reoccurring gaps by exploiting the method s inherent low displacement rank together with the development of suitable gohberg semencul representations and the use of data dependent trigonometric polynomials the proposed implementations are shown to offer a reduction of the necessary computational complexity by at least one order of magnitude numerical simulations together with theoretical complexity measures illustrate the achieved performance gain

displacement structure approach to q adic polynomial vandermonde and related matrices abstract in the present paper a new class of the so called q adic polynomial vandermonde like matrices over an arbitrary non algebraically closed field is introduced this class generalizes both the simple and the confluent polynomial vandermonde like matrices over the complex field and the q adic vandermonde and the q adic chebyshev vandermonde like matrices studied earlier by different authors three kinds of displacement structures and two kinds of fast inversion formulas are obtained for this class of matrices by using displacement structure matrix method which generalize the corresponding results of the polynomial vandermonde like and the q adic vandermonde like matrices

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

analysis of a stokes interface problem we consider a stationary stokes problem with a piecewise constant viscosity coefficient for the variational formulation of this problem we prove a well posedness result in which the constants are uniform with respect to the jump in the viscosity coefficient we apply a standard discretization with a pair of lbb stable finite element spaces the main result of the paper is an infsup result for the discrete problem that is uniform with respect to the jump in the viscosity coefficient from this we derive a robust estimate for the discretization error we prove that the mass matrix with respect to some suitable scalar product yields a robust preconditioner for the schur complement results of numerical experiments are presented that illustrate this robustness property

inverse scattering and minimal partial realizations we present an inverse scattering interpretation of the classical minimal partial realization problem posed in a slightly generalized context our approach starts by considering a canonical cascade form structure for the realization of arbitrary transfer functions where the cascade structure can be interpreted as the description of a layered wave scattering medium in this context the partial realization problem calls for a recursive process of layer identification from a given input response pair the scattering data the realization algorithm uses a causality principle to progressively determine the parameters of cascaded linear 2 ports that model the successive wave interaction layers this method for approaching the realization problem turns out to fit nicely into a framework that was also used to obtain fast structured linear estimation algorithms and cascade realizations for digital filters

on discrete schrodinger equations and their two component wave equation equivalents an approach to inverse scattering problems for discrete schrodinger equations which are discrete three term recursions is presented by systematically transforming them into discrete two component wave propagation equations the wave propagation equations permit the immediate application of certain computationally efficient and physically insightful layer peeling algorithms for inverse scattering the mapping of three term recursions to two component evolution equations is one to many because the relation between the potential sequence parametrizing schrodinger equations and the reflection coefficient sequence determining local wave interaction is a nonlinear difference equation this mapping is examined in some detail and it is used to study both direct and inverse scattering problems associated with discrete schrodinger equations

finite element methods and their convergence for elliptic and parabolic interface problems in this paper we consider the finite element methods for solving second order elliptic and parabolic interface problems in two dimensional convex polygonal domains nearly the same optimal l 2 norm and energy norm error estimates as for regular problems are obtained when the interfaces are of arbitrary shape but are smooth though the regularities of the solutions are low on the whole domain the assumptions on the finite element triangulation are reasonable and practical

approximate subspace based iterative adaptive approach for fast two dimensional spectral estimation in this paper we devise a new approach for fast implementation of two dimensional 2 d iterative adaptive approach iaa using single or multiple snapshots our underlying idea is to apply the subspace methodology in this nonparametric technique by performing the iaa on the dominant singular vectors extracted from the singular value decomposition svd or higher order svd of the multidimensional observations in doing so 2 d iaa is approximately realized by multiple steps of 1 d iaa implying that computational attractiveness is achieved particularly for large data size number of grid points and or snapshot number algorithms based on matrix and tensor operations are developed and their implementation complexities are analyzed computer simulations are also included to compare the proposed approach with the state of the art techniques in terms of resolution probability spectral estimation performance and computational requirement

complexity of multiplication with vectors for structured matrices abstract fast algorithms for computing the product with a vector are presented for a number of classes of matrices whose properties relate to the properties of toeplitz vandermonde or cauchy matrices these matrices are defined using the concept of displacement of a matrix and also for their inverses all the actions which are not dependent upon the coordinates of the input vector are singled out in a separate preprocessing stage the proposed algorithms are based on new representations of these matrices involving factor circulants

fast lcmv based methods for fundamental frequency estimation recently optimal linearly constrained minimum variance lcmv filtering methods have been applied to fundamental frequency estimation such estimators often yield preferable performance but suffer from being computationally cumbersome as the resulting cost functions are multimodal with narrow peaks and require matrix inversions for each point in the search grid in this paper we therefore consider fast implementations of lcmv based fundamental frequency estimators exploiting the estimators inherently low displacement rank of the used toeplitz like data covariance matrices using as such either the classic time domain averaging covariance matrix estimator or if aiming for an increased spectral resolution the covariance matrix resulting from the application of the recent iterative adaptive approach iaa the proposed exact implementations reduce the required computational complexity with several orders of magnitude but as we show further computational savings can be obtained by the adoption of an approximative iaa based data covariance matrix estimator reminiscent of the recently proposed quasi newton iaa technique furthermore it is shown how the considered pitch estimators can be efficiently updated when new observations become available the resulting time recursive updating can reduce the computational complexity even further the experimental results show that the performances of the proposed methods are comparable or better than that of other competing methods in terms of spectral resolution finally it is shown that the time recursive implementations are able to track pitch fluctuations of synthetic as well as real life signals

displacement structure theory and applications in this survey paper we describe how strands of work that are important in two different fields matrix theory and complex function theory have come together in some work on fast computational algorithms for matrices with what we call displacement structure in particular a fast triangularization procedure can be developed for such matrices generalizing in a striking way an algorithm presented by schur 1917 j reine angew math 147 1917 pp 205 232 in a paper on checking when a power series is bounded in the unit disc this factorization algorithm has a surprisingly wide range of significant applications going far beyond numerical linear algebra we mention among others inverse scattering analytic and unconstrained rational interpolation theory digital filter design adaptive filtering and state space least squares estimation

self organized criticality in a bulk driven one dimensional deterministic system abstract we introduce a deterministic self organized critical system that is one dimensional and bulk driven we find that there is no unique universality class associated with the system that is the critical exponents change as the parameters of the system are changed this is in contrast with the boundary driven version of the model phys rev e 61 2000 6056 in which the exponents are unique this model can be seen as a discretized version of the conservative limit of the burridge knopoff model for earthquakes

generalized chandrasekhar recursions from the generalized schur algorithm presents a new approach to the chandrasekhar recursions and some generalizations thereof the derivation uses the generalized schur recursions which are o n sup 2 recursions for the triangular factorization of n spl times n matrices having a certain toeplitz like displacement structure it is shown that when the extra structure provided by an underlying state space model is properly incorporated into the generalized schur algorithm it reduces to the chandrasekhar recursions which are o nn sup 2 recursions for estimating the n dimensional state of a time invariant or constant parameter system from n measured outputs it is further noted that the generalized schur algorithm factors more general structured matrices and this fact is readily used to extend the chandrasekhar recursions to a class of time variant state space models special cases of which often arise in adaptive filtering