initial boundary value problem for the system of compressible adiabatic flow through porous media abstract we study the initial value problem for the system of compressible adiabatic flow through porous media in the one space dimension with fixed boundary condition under the restriction on the oscillations in the initial data we establish the global existence and large time behavior for the classical solutions via the combination of characteristic analysis and energy estimate methods the time asymptotic states for the solution are found and the exponential convergence to the asymptotic states is proved it is also shown that this problem can be approximated very well time asymptotically by an initial boundary problem for the related diffusion equations obtained from the original hyperbolic system by darcy s law provided that the initial total mass is the same the difference between these two solutions tends to zero exponentially fast as time goes to infinity in the sense of h 1 the diffusive phenomena caused by damping mechanism with boundary effects are thus observed

the green s function and large time behavior of solutions for the one dimensional boltzmann equation we study the pointwise behavior of the green s function of the boltzmann equation our results reveal the particle and fluid aspects of the equation the particle aspect is represented by singular waves these waves are carried by transport equations and dominate the short time behavior of the solution we devise a picard type iteration for constructing the increasingly regular particlelike waves the fluidlike waves reveal the dissipative behavior of the type of navier stokes equations as usually seen by the chapman enskog expansion these waves are constructed as part of the long wave expansion in the spectrum of the fourier mode for the space variable the fluidlike waves represent the long time behavior of the solution as an application we obtain the pointwise description of the large time behavior of the convergence to the global maxwellian when the initial perturbation is not necessarily smooth in our analysis of the exchanges of the microscopic velocity decay and space decay we make essential use of the hard sphere models c 2004 wiley periodicals inc contents

schur recursions error formulas and convergence of rational estimators for stationary stochastic sequences an exact and approximate realization theory for estimation and model filters of second order stationary stochastic sequences is presented the properties of j lossless matrices as a unifying framework are used necessary and sufficient conditions for the exact realization of an estimation filter and a model filter as a submatrix of a j lossless system are deduced an extension of the so called schur algorithm yields an approximate j lossless realization based on partial past information about the process the geometric properties of such partial realizations and their convergence are studied finally connections with the nevanlinna pick problem are made and how the techniques presented constitute a generalization of many aspects of the levinson szego theory of partial realizations is shown as a consequence generalized recursive formulas for reproducing kernels and christoffel darboux formulas are obtained in this paper the scalar case is considered the matrix case will be considered in a separate publication

inverse eigenvalue problems for extended hessenberg and extended tridiagonal matrices in inverse eigenvalue problems one tries to reconstruct a matrix satisfying some constraints given some spectral information here two inverse eigenvalue problems are solved first given the eigenvalues and the first components of the associated eigenvectors called the weight vector an extended hessenberg matrix with prescribed poles is computed possessing these eigenvalues and satisfying the eigenvector constraints the extended hessenberg matrix is retrieved by executing particularly designed unitary similarity transformations on the diagonal matrix containing the eigenvalues this inverse problem closely links to orthogonal rational functions the extended hessenberg matrix contains the recurrence coefficients given the nodes eigenvalues poles poles of the extended hessenberg matrix and a weight vector first eigenvector components determining the discrete inner product moreover it is also sort of the inverse of the rational arnoldi algorithm instead of using the rational arnoldi method to compute a krylov basis to approximate the spectrum we will reconstruct the orthogonal krylov basis given the spectral info in the second inverse eigenvalue problem we do the same but refrain from unitarity as a result we execute possibly non unitary similarity transformations on the diagonal matrix of eigenvalues to retrieve a non symmetric extended tridiagonal matrix the algorithm will be less stable but it will be faster as the extended tridiagonal matrix admits a low cost factorization of o n n equals the number of eigenvalues whereas the extended hessenberg matrix does not again there is a close link with orthogonal function theory the extended tridiagonal matrix captures the recurrence coefficients of bi orthogonal rational functions moreover it is again sort of inverse of the nonsymmetric lanczos algorithm given spectral properties we reconstruct the two basis krylov matrices linked to the nonsymmetric lanczos algorithm

orthogonal rational functions with real coefficients and semiseparable matrices when one wants to use orthogonal rational functions orfs in system identification or control theory it is important to be able to avoid complex calculations in this paper we study orfs whose numerator and denominator polynomial have real coefficients these orfs with real coefficients rorfs appear when the poles and the interpolation points appear in complex conjugate pairs which is a natural condition further we deduce that there is a strong connection between rorfs and semiseparable matrices

structured total least squares and l2 approximation problems abstract it is shown how structured and weighted total least squares and l 2 approximation problems lead to a nonlinear generalized singular value decomposition an inverse iteration scheme to find a local minimum is proposed the emphasis of the paper is not on the convergence analysis of the algorithm rather the purpose is to illustrate its use in numerous applications in systems and control including total least squares with relative errors and or fixed elements inverse singular value problems an errors in variables variant of the kalman filter impulse response realization from noisy data h 2 model reduction h 2 system identification and calculating the largest stability radius of uncertain linear systems several numerical examples are given

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

construction of a probabilistic model for impedance matrices impedance matrices allow for the coupling of domains with very different properties and possibly modeled with different methods this paper presents the construction of a probabilistic model for such matrices using a nonparametric method that allows for the consideration of data errors as well as model errors to enable the application of this method in the case of a domain for which no finite element model is available the identification of a hidden state variables model from the knowledge of the impedance matrix at a discrete set of frequencies is also described finally the construction of the probabilistic model of the impedance of a pile foundation on a layered unbounded soil illustrates the capabilities of the method

best asymptotic profile for linear damped p system with boundary effect abstract this paper is devoted to the study of the 2 2 linear damped p system with boundary effect by a heuristic analysis we realize that the best asymptotic profile for the original solution is the parabolic solution of the ibvp for the corresponding porous media equation with a specified initial data in particular we further show the convergence rates of the original solution to its best asymptotic profile which are much better than the existing rates obtained in the previous works the approach adopted in the paper is the elementary weighted energy method with green function method together

schur complements of bezoutians and the inversion of block hankel and block toeplitz matrices abstract we derive a closed inversion formula for an np np square block hankel matrix hn 1 wi j with entries wi from the ring of the p p matrices over a field the representation of h 1n 1 relies upon a strong structure preserving property of the schur complements of the nonsingular leading principal submatrices of a certain generalized bezoutian of matrix polynomials these polynomials may be determined by computing iteratively the schur complements of the nonsingular leading principal submatrices of hn 1 in an augmented block hankel matrix h which is a bezoutian matrix up to multiplication by proper reverse matrices since the special structure of the bezoutian matrix is preserved at any step of the computation such method can be efficiently implemented at an overall computational cost of o p3n2 operations in the average case and o p3n3 operations in the worst case in the normal case a suitable modification which uses both divide and conquer strategies and fast polynomial arithmetic reaches the bound of o p3n log2 n arithmetical operations

existence and stability of planar diffusion waves for 2 d euler equations with damping abstract to study the non linear stability of a non trivial profile for a multi dimensional systems of gas dynamics the combination of the green function on estimating the lower order derivatives and the energy method for the higher order derivatives is shown to be not only useful but sometimes maybe also essential in this paper we study the stability of a planar diffusion wave for the isentropic euler equations with damping in two dimensional space by introducing an approximate green function for the linearized equations around the planar diffusion wave and by applying the energy method we prove the global existence and the l 2 convergence rate of the solution when the initial data is a small perturbation of the planar diffusion wave the decay rates of the perturbation and its lower order spatial derivatives obtained are optimal in the l 2 norm furthermore the constructed approximate green function in this paper can be used for the pointwise and the l p estimates of the solutions concerned in fact the approach by combining of the green function and energy method can be applied to other system especially when the derivatives of the coefficients in the system have certain time decay properties

lossless inverse scattering digital filters and estimation theory methods to construct rational solutions of the lossless inverse scattering lis problem for one port passive digital systems are described the first method is recursive and can be viewed as a generalization of the celebrated schur algorithm the second method is global and leads to a parametrization of what we call fundamental solutions from which all lis solutions may be constructed quite a few classical problems in estimation theory and network theory may be viewed as special cases of the lis problem with each fundamental solution there is a solution of a corresponding estimation problem leading to a prediction and a modeling filter for a given stochastic process

on the partial realization problem abstract in this paper we take a unified approach to the partial realization problem in which we seek to incorporate ideas from numerical linear algebra most of which were originally developed in other contexts we approach the partial realization problem from several different angles and explore the connections to such topics as factoriza tion of hankel matrices block tridiagonalization generalizations of the lanczos process for biorthogonalization the euclidean algorithm and the principal part con tinued fractions of arne magnus the pade table and the berlekamp masseyalgo rithm in this way we are able to clarify some previous results by rissanen kalman and others and place them in a broader context this leads to several results and concepts which we think are new our analysis is restricted to the scalar case but some definitions and formulations have been rigged to facilitate an extension to the matrix case

a new approach to the rational interpolation problem abstract we shall reformulate the classical newton pade rational interpolation problem nprip to take away several drawbacks of the newton pade approach a new recursive algorithm not reordering the interpolation points will be designed enabling us to give a parametrization of all solutions not only for the linearized rip but also for the proper rip this paper generalizes our earlier work where the pade approximation problem i e when all the interpolation points coincide at the origin was solved by reformulating it as a minimal partial realization problem van barel 1989 van barel and bultheel 1989

linear complexity parallel algorithms for linear systems of equations with recursive structure abstract a method of derivation of parallel algorithms for n 1 n 1 matrices with recursive structure is presented and applied to toeplitz hankel and other toeplitz like matrices the derived algorithms executed on o n parallel processors require o n arithmetic operations per processor

initial boundary value problem of euler equations with damping in r n abstract the asymptotic wave behavior of solution for the euler equations with damping in r n is investigated around a given constant equilibrium in this paper three classical boundary condition cases are considered here new approaches and techniques are introduced to deal with the multi dimensional case for the system for the linearized problem by comparing symbols in the transformed tangential spatial and time space we show that its green s function can be described in terms of the fundamental solution for the cauchy problem and reflected fundamental solution coupled with a boundary operator our approaches help us to simplify the green s function to the essential part and benefit the follow up nonlinear analysis for the nonlinear problem we prove the pointwise decaying rate with the help of the duhamel s principle

minimal vector pade approximation abstract we describe the minimal vector pade approximation problem which consists in finding pade approximants with a common denominator for a number of series these approximants are minimal in the sense that for a given order of approximation and a given discrepancy in numerator and denominator degrees the degree of the rational approximant is minimal properties and solution methods are derived from an associated partial realization problem

orthonormal rational function vectors in this paper we develop a matrix framework to solve the problem of finding orthonormal rational function vectors with prescribed poles open image in new window with respect to a certain discrete inner product that is defined by a set of data points open image in new window and corresponding weight vectors wi j our algorithm for solving the problem is recursive and it is of complexity open image in new window if all data points are real or lie on the unit circle then the complexity is reduced by an order of magnitude

the pointwise estimates of diffusion wave for the navier stokes systems in odd multi dimensions we study the dissipation of solutions of the isentropic navier stokes equations in odd multi dimensions pointwise estimates of the time asymptotic shape of the solutions are obtained and shown to exhibit the generalized huygen s principle our approach is based on the detailed analysis of the green function of the linearized system this is used to study the coupling of nonlinear diffusion waves

orthogonal basis functions in discrete least squares rational approximation we consider a problem that arises in the field of frequency domain system identification if a discrete time system has an input output relation y z g z u z with transter function g then the problem is to find a rational approximation n for g the data given are measurements of input and output spectra in the frequency points zk u zk y zk nk 1 together with some weight the approximation criterion is to minimize the weighted discrete least squares norm of the vector obtained by evaluating g n in the measurement points if the poles of the system are fixed then the problem reduces to a linear least squares problem in two possible ways by multiplying out the denominators and hide these in the weight which leads to the construction of orthogonal vector polynomials or the problem can be solved directly using an orthogonal basis of rational functions the orthogonality of the basis is important because if the transfer function n is represented with respect to a nonorthogonal basis then this least squares problem can be very ill conditioned even if an orthogonal basis is used but with respect to the wrong inner product e g the lebesgue measure on the unit circle numerical instability can be fatal in practice we show that both approaches lead to an inverse eigenvalue problem which forms the common framework in which fast and numerically stable algorithms can be designed for the computation of the orthonormal basis

the numerically stable reconstruction of jacobi matrices from spectral data we present an expose of the elementary theory of jacobi matrices and in particular their reconstruction from the gaussian weights and abscissas many recent works propose use of the diagonal hermitian lanczos process for this purpose we show that this process is numerically unstable we recall rutishauser s elegant and stable algorithm of 1963 based on plane rotations implement it efficiently and discuss our numerical experience we also apply rutishauser s algorithm to reconstruct a persymmetric jacobi matrix from its spectrum in an efficient and stable manner

a generalized minimal partial realization problem abstract all solutions of a generalized minimal partial realization problem are parametrized in an easy way using the basis matrix concept this basis matrix can be computed in an efficient way and is also used to solve several other interpolation problems

pade techniques for model reduction in linear system theory a survey abstract techniques of pade approximation and continued fractions have been used often in model reduction problems an extensive bibliography on this topic is given the ideas are explained for the simple situation of a scalar function where no singular blocks appear in the pade table extensions to the matrix case and the multivariable case are not explained in detail

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

a look ahead algorithm for the solution of general hankel systems the solution of systems of linear equations with hankel coefficient matrices can be computed with onlyo n 2 arithmetic operations as compared too n 3 operations for the general cases however the classical hankel solvers require the nonsingularity of all leading principal submatrices of the hankel matrix the known extensions of these algorithms to general hankel systems can handle only exactly singular submatrices but not ill conditioned ones and hence they are numerically unstable in this paper a stable procedure for solving general nonsingular hankel systems is presented using a look ahead technique to skip over singular or ill conditioned submatrices the proposed approach is based on a look ahead variant of the nonsymmetric lanczos process that was recently developed by freund gutknecht and nachtigal we first derive a somewhat more general formulation of this look ahead lanczos algorithm in terms of formally orthogonal polynomials which then yields the look ahead hankel solver as a special case we prove some general properties of the resulting look ahead algorithm for formally orthogonal polynomials these results are then utilized in the implementation of the hankel solver we report some numerical experiments for hankel systems with ill conditioned submatrices

blind separation of speech mixtures via time frequency masking binary time frequency masks are powerful tools for the separation of sources from a single mixture perfect demixing via binary time frequency masks is possible provided the time frequency representations of the sources do not overlap a condition we call w disjoint orthogonality we introduce here the concept of approximate w disjoint orthogonality and present experimental results demonstrating the level of approximate w disjoint orthogonality of speech in mixtures of various orders the results demonstrate that there exist ideal binary time frequency masks that can separate several speech signals from one mixture while determining these masks blindly from just one mixture is an open problem we show that we can approximate the ideal masks in the case where two anechoic mixtures are provided motivated by the maximum likelihood mixing parameter estimators we define a power weighted two dimensional 2 d histogram constructed from the ratio of the time frequency representations of the mixtures that is shown to have one peak for each source with peak location corresponding to the relative attenuation and delay mixing parameters the histogram is used to create time frequency masks that partition one of the mixtures into the original sources experimental results on speech mixtures verify the technique example demixing results can be found online at http alum mit edu www rickard bss html

initial boundary value problem for p system with damping in half space abstract in this paper the initial boundary value problem for p system with damping in half space is studied with a posed mix boundary condition the fundamental solution green s function for cauchy problem is constructed with a sharp decaying structure and a precise capture of the singularity by a singularity removal process later the symbols of both fundamental solution and green s function for initial boundary value problem are obtained with transformed variable s and spatial variable x while in this level the green s function could be decomposed into fundamental solution and boundary operator thus with the study of boundary operator and previous precise information about the fundamental solution the pointwise structure as well as the singular structure of the green s function is established finally the nonlinear stability is obtained by the green s function and a priori estimate from energy method

l p convergence rates of planar waves for multi dimensional euler equations with damping abstract in this paper the l p convergence rates of planar diffusion waves for multi dimensional euler equations with damping are considered the analysis relies on a newly introduced frequency decomposition and green function based energy method it is a combination of the l p estimate on the low frequency component by using an approximate green function and l 2 estimate on the high frequency component through the energy method by noticing that the low frequency component in the approximate green function has the algebraic decay which governs the large time behavior while the high frequency component has the exponential decay but with singularity their combination leads to a global algebraic decay estimate to use the decay property only of the low frequency component in the approximate green function avoids the singularity in the high frequency component so that it simplifies and improves the previous works on this system this new approach of the combination of the green function and energy method through the frequency decomposition can also be applied to the hyperbolic parabolic systems satisfying the kawashima condition and also the systems whose derivatives of the coefficients have suitable time decay properties

large time behavior of solutions for compressible euler equations with damping in r 3 we consider the long time behavior and optimal decay rates of global strong solutions for the isentropic compressible euler equations with damping in r3 in the present paper when the regular initial data belong to some sobolev space hl r3 b 1 s r3 with l 4 and s 0 1 we show that the density of the system converges to its equilibrium state at the rates 1 t 34 s2 in the l2 norm or 1 t 32 s2 in the l norm respectively the momentum of the system decays at the rates 1 t 54 s2 in the l2 norm or 1 t 2 s2 in the l norm respectively which are shown to be optimal for the compressible euler equations with damping

well posedness of the ibvp for 2 d euler equations with damping abstract in this paper we focus on the initial boundary value problem of the 2 d isentropic euler equations with damping we prove the global in time existence of classical solution to the initial boundary value problem for small smooth initial data by the method of local existence of solution combined with a priori energy estimates where the appropriate boundary condition plays an important role

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

blind adaptation of zero forcing projections and oblique pseudo inverses for subspace detection and estimation when interference dominates noise in much of modern radar sonar and wireless communication it seems more reasonable to model measurement noise as subspace interference plus broadband noise than as colored noise this observation leads naturally to a variety of detection and estimation problems in the linear statistical model to solve these problems one requires oblique pseudo inverses oblique projections and zero forcing orthogonal projections the problem is that these operators depend on knowledge of signal and interference subspaces and this information is often not at hand more typically the signal subspace is known but the interference subspace is unknown we prove a theorem that allows these operators to be estimated directly from experimental data without knowledge of the interference subspace as a byproduct the theorem shows how signal subspace covariance may be estimated when the strict identities of the theorem are approximated then the detectors estimators and beamformers of this paper take on the form of adaptive subspace estimators detectors and capon beamformers all of which are reduced in rank the fundamental operator turns out to be a certain reduced rank wiener filter which we clarify in the course of our derivations the results of this paper form a foundation for the rapid adaptation of receivers that are then used for detection and estimation they may be applied to detection and estimation in radar sonar and hyperspectral imaging and to data decoding in multiuser communication receivers

hyperbolic to parabolic relaxation theory for quasilinear first order systems abstract in this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type in particular we obtain a complete theory for the 2 2 systems of genuinely nonlinear hyperbolic balance laws in 1 d with a strong dissipative term a different method which combines the div curl lemma with accretive operators is then applied to study the limiting profiles in the case of nonhomogeneous isentropic gas dynamics we also investigate relaxation results for some 2 d cases which include the cattaneo model for nonlinear heat conduction and the compressible euler flow moreover convergence result is also obtained for general semilinear systems in 1 d

a new approach to the rational interpolation problem the vector case we generalize our earlier results on rational interpolation which were given in van barel and bultheel this journal 1990 for the scalar case and in bultheel and van barel 1990 for the vector case when all the interpolation points coincide to the case of vector data given at arbitrary points that may coincide or not this is the vector valued newton pade problem we give a recursive algorithm which has the important advantage over other algorithms that we do not need a reordering of the given interpolation data to overcome a singularity in the interpolation table not even in the nonnormal vector case it also generates all the information needed to give all solutions of the problem

discrete linearized least squares rational approximation on the unit circle abstract we already generalized the rutishauser gragg harrod reichel algorithm for discrete least squares polynomial approximation on the real axis to the rational case in this paper a new method for discrete least squares linearized rational approximation on the unit circle is presented it generalizes the algorithms of reichel ammar gragg for discrete least squares polynomial approximation on the unit circle to the rationale case the algorithm is fast in the sense that it requires order m computation time where m is the number of data points and is the degree of the approximant we describe how this algorithm can be implemented in parallel examples illustrate the numerical behavior of the algorithm

half space problem for euler equations with damping in 3 d abstract in this paper we consider the half space problem for euler equations with damping in 3 d we restudy the fundamental solution for the cauchy problem to obtain an exponentially sharp pointwise structure and a clear decomposition of the singular regular components later both green s function for initial boundary value problem and fundamental solutions for cauchy problems are investigated in the transformed domain after laplace transform the symbols are obtained and a connection between green s function and fundamental solutions are established for the pointwise space time structure of green s function finally the sharp estimates for green s function together with a priori estimates from the energy method for high order derivatives result in the nonlinear stability of the solution and also the decaying rates

a convex optimization approach to the rational covariance extension problem in this paper we present a convex optimization problem for solving the rational covariance extension problem given a partial covariance sequence and the desired zeros of the modeling filter the poles are uniquely determined from the unique minimum of the corresponding optimization problem in this way we obtain an algorithm for solving the covariance extension problem as well as a constructive proof of georgiou s seminal existence result and his conjecture a stronger version of which we have resolved in byrnes et al ieee trans automat control ac 40 1995 pp 1841 1857

a parallel algorithm for discrete least squares rational approximation a new method for discrete least squares linearized rational approximation is presented it generalizes the algorithm of rutishauser gragg harrod reichel for discrete least squares polynomial approximation to the rational case the algorithm is fast in the sense that it requires orderm computation time wherem is the number of data points and is the degree of the approximant we describe how this algorithm can be implemented in parallel

large time behavior for the system of compressible adiabatic flow through porous media in r3 abstract the cauchy problem of the system of compressible adiabatic flow through porous media in r 3 is considered we obtain the global existence and large time behavior of the solution when the initial data is close to its equilibrium in h 3 norm this is a continuing work of 31 where due to non dissipative property of the entropy s an additional assumption that the initial data is bounded in l 1 norm plays a key role in closing the a priori energy estimates and hence establishing the global existence of the solution in this paper to remove this assumption we first decompose the solution u into high frequency part u h and low frequency part u l then by constructing delicate energy functionals for u h and optimal decay rates for u l we can get the desired energy estimates to close the a priori assumption furthermore we get the optimal l 2 l 2 decay rate of the solution and show that the velocity decays faster than the density

signal processing applications of oblique projection operators oblique projection operators are used to project measurements onto a low rank subspace along a direction that is oblique to the subspace they may be used to enhance signals while nulling interferences in the paper the authors give several basic results for oblique projections including formulas for constructing oblique projections with desired range and null space they analyze the algebra and geometry of oblique projections in order to understand their properties they then show how oblique projections can be used to separate signals from structured noise such as impulse noise damped or undamped interfering sinusoids such as power line interference and narrow band noise in some of the problems addressed the oblique projection provides an alternative way to implement an already known solution expressing these solutions as oblique projections brings geometrical insight to the study of the solution the geometry of oblique projections enables one to compute performance in terms of angles between signal and noise subspaces as a special case of removing impulse noise the authors can use oblique projections to interpolate missing data samples in array processing oblique projections can be used to simultaneously steer beams and nulls in communications oblique projections can be used to remove intersymbol interference

lp convergence rate to nonlinear diffusion waves for p system with damping abstract in this paper we study the p system with frictional damping and show that the solutions time asymptotically tend to the nonlinear diffusion waves governed by the classical darcy s law by introducing an approximate green function we obtain the optimal l p 2 p convergence rate of the solution which is a perturbation of the nonlinear diffusion wave to the hyperbolic system

underdetermined blind source separation based on sparse representation this paper discusses underdetermined i e with more sources than sensors blind source separation bss using a two stage sparse representation approach the first challenging task of this approach is to estimate precisely the unknown mixing matrix in this paper an algorithm for estimating the mixing matrix that can be viewed as an extension of the duet and the tifrom methods is first developed standard clustering algorithms e g k means method also can be used for estimating the mixing matrix if the sources are sufficiently sparse compared with the duet the tifrom methods and standard clustering algorithms with the authors proposed method a broader class of problems can be solved because the required key condition on sparsity of the sources can be considerably relaxed the second task of the two stage approach is to estimate the source matrix using a standard linear programming algorithm another main contribution of the work described in this paper is the development of a recoverability analysis after extending the results in a necessary and sufficient condition for recoverability of a source vector is obtained based on this condition and various types of source sparsity several probability inequalities and probability estimates for the recoverability issue are established finally simulation results that illustrate the effectiveness of the theoretical results are presented

convergence to the barenblatt solution for the compressible euler equations with damping and vacuum we study the asymptotic behavior of a compressible isentropic flow through a porous medium when the initial mass is finite the model system is the compressible euler equation with frictional damping as t the density is conjectured to obey the well known porous medium equation and the momentum is expected to be formulated by darcy s law in this paper we give a definite answer to this conjecture without any assumption on smallness or regularity for the initial data we prove that any l weak entropy solution to the cauchy problem of damped euler equations with finite initial mass converges strongly in lp with decay rates to matching barenblatt s profile of the porous medium equation the density function tends to the barenblatt s solution of the porous medium equation while the momentum is described by darcy s law

a deflation procedure for subspace decomposition a general deflation framework is described for the separation of a desired signal subspace of arbitrary dimensions from noisy multichannel observations the method simultaneously uses single and multichannel priors to split the desired and undesired subspaces even for coplanar intersecting subspaces by appropriate use of signal priors it can even extract signals from degenerate mixtures of signals and noise recorded from a few number of channels in low snr scenarios without the reduction of the data dimensions as a case study the performance of the proposed method is studied for the problem of extracting fetal cardiac signals from maternal abdominal recordings over simulated and real data a second case study deals with the degenerate problem of extracting diaphragmatic electromyogram from electrocardiograph artifacts a provisional patent application based on this method has been filed

asymptotic behavior of the solutions to the damped compressible euler equations with vacuum abstract the asymptotic behavior of solutions of the damped compressible euler equations is conjectured to obey to the famous porous media equations pmes the previous works on this topic concern the case away from vacuum where the system is strictly hyperbolic in present paper we prove that the l entropy weak solution with vacuum obtained by the compensated compactness theory converges strongly in l loc p 1 p space to the unique similarity solution of the related pme as time goes to infinity

the pointwise estimates of solutions for euler equations with damping in multi dimensions we study the time asymptotic behavior of solutions for the isentropic euler equations with damping in multi dimensions the global existence and pointwise estimates of the solutions are obtained furthermore we obtain the optimal lp 1 p convergence rate of the solution when it is a perturbation of a constant state our approach is based on a detailed analysis of the green function of the linearized system and some energy estimates

convergence to strong nonlinear diffusion waves for solutions of p system with damping this paper is concerned with the p system with frictional damping and our main purpose is two fold first we show that for a certain class of given large initial data nu 0 x u 0 x the cauchy problem 1 1 1 2 admits a unique global smooth solution nu t x u t x and such a solution tends time asymptotically at the optimal l p 2 less than or equal to p less than or equal to infinity decay rates to the corresponding nonlinear diffusion wave over bar t x u over bar t x governed by the classical darcy s law provided that the corresponding prescribed initial error function v 0 x u 0 x ties in h 3 x h 2 r boolean and l 1 x l 1 r compared with former results in this direction obtained by l hsiao and t p liu 1992 comm math phys 143 599 605 k nishihara 1996 j differential equations 131 171 188 and k nishihara w k wang and t yang 2000 j differential equations 161 191 218 our main novelty lies in the facts that the nonlinear diffusion wave over bar t x u over bar t x need not to be weak and v 0 x u 0 x can be chosen arbitrarily large secondly we show that the nonlinear diffusion waves over bar t x u over bar t x are nonlinear stable provided that the strength or the nonlinear diffusion waves is weak and that the initial disturbance v 0 x u 0 x satisfies the assumption that parallel tov 0xx x parallel to l infinity parallel tou 0x x parallel to l infinity is sufficiently small we also show that the smallness assumption imposed oil the strength of the diffusion waves is a necessary condition to guarantee the nonlinear stability result and compared with the corresponding results obtained by l hsiao and t p liu 1992 comm math phys 143 599 605 the smallness conditions we imposed on the initial disturbance are much more weaker c 2001 academic press

global existence and large time behavior for the system of compressible adiabatic flow through porous media in r 3 abstract the system of compressible adiabatic flow through porous media is considered in r 3 in the present paper the global existence and uniqueness of classical solutions are obtained when the initial data is near its equilibrium we also show that the pressure of the system converges to its equilibrium state at the same l 2 rate 1 t 3 4 as the navier stokes equations without heat conductivity but the velocity of the system decays at the l 2 rate 1 t 5 4 which is faster than the l 2 rate 1 t 3 4 for the navier stokes equations without heat conductivity duan and ma 2008 3

convergence rate for compressible euler equations with damping and vacuum we study the asymptotic behavior of l weak entropy solutions to the compressible euler equations with damping and vacuum previous works on this topic are mainly concerned with the case away from the vacuum and small initial data in the present paper we prove that the entropy weak solution strongly converges to the similarity solution of the porous media equations in lp r 2 p with decay rates the initial data can contain vacuum and can be arbitrary large a new approach is introduced to control the singularity near vacuum for the desired estimates

numerically robust transfer function modeling from noisy frequency domain data using vector orthogonal polynomials as basis functions for the representation of the rational form of a linear time invariant system in frequency domain identification problems it is shown that the notorious numerical ill conditioning of these maximum likelihood problems can be overcome completely for the identification of high order 100 100 systems operating over a wide frequency band or even in the situation of over or undermodeling condition numbers less than ten are reported for real measurements

darcy s law as long time limit of adiabatic porous media flow abstract it is conjectured that darcy s law governs the motion of compressible porous media flow in large time this has been justified for one dimensional isentropic flows in this work we show the conjecture is true for one dimensional adiabatic flows with generic small smooth initial data

unitary rank structured matrices in this paper we describe how one can represent a unitary rank structured matrix in an efficient way as a product of elementary unitary or givens transformations we also provide some basic operations for manipulating the representation such as the transition to zero creating form the transition to a unitary givens weight representation as well as an internal pull through process of the two branches of the representation finally we characterize how to determine the shift correction term to the rank structure and we provide some applications to this result

a new formal approach to the rational interpolation problem an elegant and fast recursive algorithm is developed to solve the rational interpolation problem in a complementary way compared to existing methods we allow confluent interpolation points poles and infinity as one of the interpolation points not only one specific solution is given but a nice parametrization of all solutions we also give a linear algebra interpretation of the problem showing that our algorithm can also be used to handle a specific class of structured matrices

green s functions of wave equations in mathbb r n_ times mathbb r _ we study the d alembert equation with a boundary we introduce the notions of rayleigh surface wave operators delayed advanced mirror images wave recombinations and wave cancellations this allows us to obtain the complete and simple formula of the green s functions for the wave equation with the presence of various boundary conditions we are able to determine whether a rayleigh surface wave is active or virtual and study the lacunas of the wave equation in three dimensional with the presence of a boundary in the case of a virtual rayleigh surface wave

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

eigenvalue computation for unitary rank structured matrices in this paper we describe how to compute the eigenvalues of a unitary rank structured matrix in two steps first we perform a reduction of the given matrix into hessenberg form next we compute the eigenvalues of this resulting hessenberg matrix via an implicit qr algorithm along the way we explain how the knowledge of a certain shift correction term to the structure can be used to speed up the qr algorithm for unitary hessenberg matrices and how this observation was implicitly used in a paper due to william b gragg we also treat an analogue of this observation in the hermitian tridiagonal case

optimally conditioned instrumental variable approach for frequency domain system identification accurate frequency domain system identification demands for reliable computational algorithms the aim of this paper is to develop a new algorithm for parametric system identification with favorable convergence properties and optimal numerical conditioning recent results in frequency domain instrumental variable identification are exploited which lead to enhanced convergence properties compared to classical identification algorithms in addition bi orthonormal polynomials with respect to a data dependent bi linear form are introduced for system identification hereby optimal numerical conditioning of the relevant system of equations is achieved this is shown to be particularly important for the class of instrumental variable algorithms for which numerical conditioning is typically quadratic compared to alternative frequency domain identification algorithms superiority of the proposed algorithm is demonstrated by means of both simulation and experimental results

tight bounds for the trace of a matrix product we propose a family of new upper and lower bounds for the trace of the matrix product ab when a or b is symmetric those bounds depend on a scalar parameter and both converge monotonically to tr ab when this parameter vanishes thus providing arbitrary close approximations even large values of the parameter yield very good bounds

vector valued rational interpolants i it is shown explicitly that the samelson inverse may be used to define vector valued thiele type rational interpolants and the equivalence with claessens algorithm is established for the special case of vector valued pade approximants the general form of mccleod s theorem follows as a corollary

viability of methods for generating stable reduced order models various methods for generating stable reduced order models are shown to have a serious disadvantage in that the reduced model may approximate the nondominant poles of the system and hence lead to erroneous approximations an example is given to compare these methods with the standard pade approximation method for which this disadvantage does not exist

recursiveness in matrix rational interpolation problems abstract we consider the problem of computing solutions to a variety of matrix rational interpolation problems these include the partial realization problem for matrix power series and newton pade hermite pade simultaneous pade m pade and multipoint pade approximation problems along with their matrix generalizations a general recurrence relation is given for solving these problems unlike other previous recursive methods our recurrence works along arbitrary computational paths when restricted to specific paths the recurrence relation generalizes previous work of antoulas cabay and labahn beckermann van barel and bultheel and gutknecht along with others our results rely on the concept of extended m pade approximation introduced in this paper this is a natural generalization of the two point pade approximation problem extended to multiple interpolation points including infinity and matrix laurent and newton series by using module theoretic techniques we determine complete parameterizations of all solutions to this problem our recurrence relation then efficiently computes these parameterizations this recursion requires no conditions on the input data we also discuss the concept of duality which was shown to be of particular interest for a stable computation of those approximants finally we show the invariance of our approximation problem under linear transformations of the extended complex plane

a unifying construction of orthonormal bases for system identification this paper develops a general and very simple construction for complete orthonormal bases for system identification this construction provides a unifying formulation of many previously studied orthonormal bases since the common fir and recently popular laguerre and two parameter kautz model structures are restrictive special cases of the construction presented here however in contrast to these special cases the basis vectors in the unifying construction of this paper can have arbitrary placement of pole position according to the prior information the user wishes to inject results characterizing the completeness of the bases and the accuracy properties of models estimated using the bases are provided

half space problem of the system of compressible adiabatic flow through porous media in multi d abstract in this paper we consider the half space problem for the system of compressible adiabatic flow through porous media in 2 d and 3 d combining energy method green s function method and bootstrap method one establishes the decaying energy estimates which lead to global existence and optimal l 2 decaying rate of the solution finally for more large time information especially in spatial variables one applies green s function solution representation obtained by duhamel s principle and a priori estimate from energy method to obtain the space time pointwise structure of the solution

existence and asymptotic behavior of c1 solutions to the multi dimensional compressible euler equations with damping abstract in this paper the existence and asymptotic behavior of c 1 solutions to the multi dimensional compressible euler equations with damping on the framework of besov space are considered comparing with the well posedness results of sideris thomases wang t sideris b thomases d h wang long time behavior of solutions to the three dimensional compressible euler with damping comm partial differential equations 28 2003 953 978 we weaken the regularity assumptions on the initial data the global existence lies on a crucial a priori estimate which is obtained by the spectral localization method the main analytic tools are the littlewood paley decomposition and bony s paraproduct formula

continued fractions associated with the newton pade table we discuss first the block structure of the newton pade table or rational interpolation table corresponding to the double sequence of rational interpolants for the data zk h zk k 0 the m n entry of this table is the rational function of type m n solving the linearized rational interpolation problem on the firstm n 1 data we then construct continued fractions that are associated with either a diagonal or two adjacent diagonals of this newton pade table in such a way that the convergents of the continued fractions are equal to the distinct entries on this diagonal or this pair of diagonals respectively the resulting continued fractions are generalizations of thiele fractions and of magnus sp fractions a discussion of an some new results on related algorithms of werner and graves morris and hopkins are also given

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

rational interpolation and the euclidean algorithm abstract a general framework leading to a parametrization of all rational functions which interpolate a given set of pairs of points is investigated this framework is based on the euclidean algorithm the resulting parametrization has the property that it keeps track of the complexity of both the numerator and of the denominator polynomials of the interpolating functions the cauchy interpolation problem and the related pade approximation problem can be treated within this framework

rational approximation in linear systems and control abstract in this paper we want to describe some examples of the active interaction that takes place at the border of rational approximation theory and linear system theory these examples are mainly taken from the period 1950 1999 and are described only at a skindeep level in the simplest possible scalar case we give comments on generalizations of these problems and how they opened up new ranges of research that after a while lived their own lives we also describe some open problems and future work that will probably continue for some years after 2000

local existence with physical vacuum boundary condition to euler equations with damping abstract in this paper we consider the local existence of solutions to euler equations with linear damping under the assumption of physical vacuum boundary condition by using the transformation introduced in lin and yang methods appl anal 7 3 2000 495 to capture the singularity of the boundary we prove a local existence theorem on a perturbation of a planar wave solution by using littlewood paley theory and justifies the transformation introduced in liu and yang 2000 in a rigorous setting

the 3d compressible euler equations with damping in a bounded domain abstract we proved global existence and uniqueness of classical solutions to the initial boundary value problem for the 3d damped compressible euler equations on bounded domain with slip boundary condition when the initial data is near its equilibrium time asymptotically the density is conjectured to satisfy the porous medium equation and the momentum obeys to the classical darcy s law based on energy estimate we showed that the classical solution converges to steady state exponentially fast in time we also proved that the same is true for the related initial boundary value problem of porous medium equation and thus justified the validity of darcy s law in large time

dynamics of structures coupled with elastic media a review of numerical models and methods abstract this paper reviews issues and developments in the field of structure environment interaction problems in which the environment is an elastic body possibly unbounded it covers in particular the fields of soil structure interaction ground borne noise and vibration emitted by transportation systems and wave diffraction by obstacles in an elastic medium the general setting for a linear bounded structure coupled to an unbounded linear environment through a bounded interface is first recalled and the domain decomposition technique classically used for its description is put up extensions for the cases of nonlinear structure and uncertain environment are then discussed finally the ongoing research in the fields of unbounded interface moving interface and multiple interfaces are reviewed and summarized

on the problem of stable rational interpolation abstract aspects of the stability issue in connection with rational interpolation are investigated in particular it is shown that unconstrained interpolation of a given set of points together with an associated mirror image set of points yields a one parameter family of stable interpolating functions as an application it is also shown that if a certain number of markov parameters are given by appropriate choice of the moments stable realizations are obtained