adaptive filtering in subbands with critical sampling analysis experiments and application to acoustic echo cancellation an exact analysis of the critically subsampled two band modelization scheme is given and it is demonstrated that adaptive cross filters between the subbands are necessary for modelization with small output errors it is shown that perfect reconstruction filter banks can yield exact modelization these results are extended to the critically subsampled multiband schemes and important computational savings are seen to be achieved by using good quality filter banks the problem of adaptive identification in critically subsampled subbands is considered and an appropriate adaptation algorithm is derived the authors give a detailed analysis of the computational complexity of all the discussed schemes and experimentally verify the theoretical results that are obtained the adaptive behavior of the subband schemes that were tested is discussed

a projection method for generalized eigenvalue problems using numerical integration in this paper we propose a method for finding certain eigenvalues of a generalized eigenvalue problem that lie in a given domain of the complex plane the proposed method projects the matrix pencil onto a subspace associated with the eigenvalues that are located in the domain via numerical integration

solution of the helmholtz eigenvalue problem via the boundary element method the numerical solution of the helmholtz eigenvalue problem is considered the application of the boundary element method reduces it to that of a non linear eigenvalue problem through a polynomial approximation with respect to the wavenumber the non linear eigenvalue problem is reduced to a standard generalized eigenvalue problem the method is applied to the test problems of a three dimensional sphere with an axisymmetric boundary condition and a two dimensional square

on solving constrained optimization problems with neural networks a penalty method approach deals with the use of neural networks to solve linear and nonlinear programming problems the dynamics of these networks are analyzed in particular the dynamics of the canonical nonlinear programming circuit are analyzed the circuit is shown to be a gradient system that seeks to minimize an unconstrained energy function that can be viewed as a penalty method approximation of the original problem next the implementations that correspond to the dynamical canonical nonlinear programming circuit are examined it is shown that the energy function that the system seeks to minimize is different than that of the canonical circuit due to the saturation limits of op amps in the circuit it is also noted that this difference can cause the circuit to converge to a different state than the dynamical canonical circuit to remedy this problem a new circuit implementation is proposed

a contour integral approach to the computation of invariant pairs abstract we study some aspects of the invariant pair problem for matrix polynomials as introduced by betcke and kressner 3 and by beyn and thummler 6 invariant pairs extend the notion of eigenvalue eigenvector pairs providing a counterpart of invariant subspaces for the nonlinear case we compute formulations for the condition numbers and the backward error for invariant pairs and solvents we then adapt the sakurai sugiura moment method 1 to the computation of invariant pairs including some classes of problems that have multiple eigenvalues numerical refinement via a variant of newton s method is also studied furthermore we investigate the relation between the matrix solvent problem and the triangularization of matrix polynomials

sliding modes in solving convex programming problems sliding modes are used to analyze a class of dynamical systems that solve convex programming problems the analysis is carried out using concepts from the theory of differential equations with discontinuous right hand sides and lyapunov stability theory it is shown that the equilibrium points of the system coincide with the minimizers of the convex programming problem and that irrespective of the initial state of the system the state trajectory converges to the solution set of the problem the dynamic behavior of the systems is illustrated by two numerical examples

coupled fe be method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain summary for thin elastic structures submerged in heavy fluid e g water a strong interaction between the structural domain and the fluid domain occurs and significantly alters the eigenfrequencies therefore the eigenanalysis of the fluid structure interaction system is necessary in this paper a coupled finite element and boundary element fe be method is developed for the numerical eigenanalysis of the fluid structure interaction problems the structure is modeled by the finite element method the compressibility of the fluid is taken into consideration and hence the helmholtz equation is employed as the governing equation and solved by the boundary element method bem the resulting nonlinear eigenvalue problem is converted into a small linear one by applying a contour integral method adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenvalues of interest the burton miller formulation is applied to tackle the fictitious eigenfrequency problem of the bem and the optimal choice of its coupling parameter is investigated for the coupled fe be method numerical examples are given and discussed to demonstrate the effectiveness and accuracy of the developed fe be method copyright 2016 john wiley sons ltd

nonlinear eigenvalue problems and contour integrals in this paper beyn s algorithm for solving nonlinear eigenvalue problems is given a new interpretation and a variant is designed in which the required information is extracted via the canonical polyadic decomposition of a hankel tensor a numerical example shows that the choice of the filter function is very important particularly with respect to where it is positioned in the complex plane

the exponentially convergent trapezoidal rule it is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line the mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity it is linked with computational methods all across scientific computing including algorithms related to inverse laplace transforms special functions complex analysis rational approximation integral equations and the computation of functions and eigenvalues of matrices and operators

a new delayless subband adaptive filter structure adaptive subband techniques have been developed to reduce complexity and slow convergence problems of the traditional fullband high order adaptive filters some of the disadvantages often encountered in most of the proposed architectures are the effect of aliasing associated with the multirate structure which is a source of error in the modeling of the unknown system and the delay introduced in the signal path we present a new delayless maximally decimated structure where the optimal subband filters are related to the wideband system in a closed form they make use of a special dft analysis filterbank where the polyphase components of the prototype filter represent fractional delays so that there is no need for adaptive cross filters and the unknown system can modeled perfectly in a closed loop scheme we interpret the proposed structure as a special case of a block adaptive filter with lower computational complexity than the conventional fullband lms algorithm some computer simulations are presented in order to verify the good features of the proposed structure

on a convex parameter space method for linear control design of uncertain systems this paper presents a new procedure for continuous and discrete time linear control systems design it consists of the definition of a convex programming problem in the parameter space that when solved provides the feedback gain one of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation yielding solutions to problems that have raised a great deal of interest within the last few years this is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices in this last case necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and to the authors knowledge this is one of the first numerical procedures able to handle and solve this interesting design problem for high order continuous time or discrete time linear models the theory is illustrated by examples

an integral method for solving nonlinear eigenvalue problems we propose a numerical method for computing all eigenvalues and the corresponding eigenvectors of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane the method uses complex integrals of the resolvent operator applied to at least k column vectors where k is the number of eigenvalues inside the contour the theorem of keldysh is employed to show that the original nonlinear eigenvalue problem reduces to a linear eigenvalue problem of dimension k no initial approximations of eigenvalues and eigenvectors are needed the method is particularly suitable for moderately large eigenvalue problems where k is much smaller than the matrix dimension we also give an extension of the method to the case where k is larger than the matrix dimension the quadrature errors caused by the trapezoid sum are discussed for the case of analytic closed contours using well known techniques it is shown that the error decays exponentially with an exponent given by the product of the number of quadrature points and the minimal distance of the eigenvalues to the contour

a novel numerical method to determine the algebraic multiplicity of nonlinear eigenvalues we generalize the algebraic multiplicity of the eigenvalues of nonlinear eigenvalue problems neps to the rational form and give the extension of the argument principle in addition we propose a novel numerical method to determine the algebraic multiplicity of the eigenvalues of the neps in a given region by the contour integral method finally some numerical experiments are reported to illustrate the effectiveness of our method

a variable structure convex programming based control approach for a class of uncertain linear systems a variable structure convex programming based control for a class of linear uncertain systems with accessible state is presented in this note a convex programming problem is solved on line by reformulating the problem in terms of a piecewise smooth penalty function and relying on a suitable analog variable structure system implementing the gradient procedure in this way the controlled system reference movement optimal with respect to a pre specified scalar convex cost function and a set of suitable equality and inequality constraints is generated an inner control loop aimed at the finite time exact tracking of the reference movement is also designed as a result the controlled system trajectory starting in the feasible region there remains and the optimal movement in the feasible region is proved to be an asymptotically stable equilibrium point of the controlled system

localization theorems for nonlinear eigenvalue problems let t omega rightarrow mathbb c n times n be a matrix valued function that is analytic on some simply connected domain omega subset mathbb c a point lambda in omega is an eigenvalue if the matrix t lambda is singular in this article we describe new localization results for nonlinear eigenvalue problems that generalize gershgorin s theorem pseudospectral inclusion theorems and the bauer fike theorem we use our results to analyze three nonlinear eigenvalue problems an example from delay differential equations a problem due to hadeler and a quantum resonance computation

stabilizing receding horizon control of nonlinear time varying systems a receding horizon control scheme for nonlinear time varying systems is proposed which is based on a finite horizon optimization problem with a terminal state penalty the penalty is equal to the cost that would be incurred over an infinite horizon by applying a locally stabilizing linear control law to the nonlinear system assuming only stabilizability of the linearized system around the desired equilibrium the new scheme ensures exponential stability of the equilibrium as the length of the optimization horizon goes from zero to infinity the domain of attraction moves from the basin of attraction of the linear controller toward the basin of attraction of the infinite horizon nonlinear controller stability robustness in the face of system perturbations is also established

a convex optimization approach to fixed order controller design for disturbance rejection in siso systems the problem of rejection of persistent unknown but bounded disturbances can be solved using the well known l sup 1 design approach however in spite of its success this theory suffers from the fact that the resulting controller may have arbitrarily high order even in the state feedback case in addition system performance is optimized under the assumption of zero initial conditions in this paper we propose a new approach to the problem of synthesizing fixed order controllers to optimally reject persistent disturbances the main result of the paper shows that this approach leads to a finite dimensional convex optimization problem that can be efficiently solved

numerical algorithms based on analytic function values at roots of unity let f z be an analytic or meromorphic function in the closed unit disk sampled at the n th roots of unity based on these data how can we approximately evaluate f z or f m z at a point z in the disk how can we calculate the zeros or poles of f in the disk these questions exhibit in the purest form certain algorithmic issues that arise across computational science in areas including integral equations partial differential equations and large scale linear algebra we analyze some of the possibilities and emphasize the distinction between algorithms based on polynomial or rational interpolation and those based on trapezoidal rule approximations of cauchy integrals we then show how these developments apply to the problem of computing the eigenvalues in the disk of a matrix of large dimension finally we highlight the power of rational in comparison with polynomial approximations for some of these problems

polynomial transform implementation of digital filter banks this paper investigates the use of polynomial transforms for the implementation of uniform digital bandpass filter banks the technique is based upon a decomposition of the n bandpass filters into a set of real polyphase filters followed by a dct discrete cosine transform of size n the dct is converted into a dft discrete fourier transform of size n and the polyphase filters are evaluated by dft s this procedure yields a two dimensional dft which is computed by a polynomial transform and odd dft s we show that this technique reduces significantly the number of arithmetic operations when compared to conventional methods and yields a regular structure in which most of the computations are performed with fft type algorithms

new polynomial transform algorithms for multidimensional dft s and convolutions this paper introduces a new method for the computation of multidimensional dft s by polynomial transforms the method which maps mtiltidimensional dft s into one dimensional odd time dft s by use of inverse polynomial transforms is shown to be significantly more efficient than the conventional row column method from the standpoint of the number of arithmetic operations and quantization noise the relationship between dft and convolution algorithms using polynomial transforms is clarified and new convolution algorithms with reduced computational complexities are proposed

robust time optimal control of constrained linear systems a version of dynamic programming which computes level sets of the value function rather than the value function set itself is used to design robust non linear controllers for linear discrete time dynamical systems subject to hard constraints on controls and states the controller stabilizes the system and steers all trajectories emanating in a prescribed set to a control invariant set in minimum time for the robust regulator problem the control invariant terminal set is a neighborhood preferably small of the origin for the robust tracking problem the control invariant terminal set is a neighborhood of the invariant set in which the tracking error is zero two non linear controllers which utilize the level sets of the value function are described the first requires the controller to solve on line a modest linear program whose dimension is approximately the same as that of the control variable the second decomposes each level set into a set of simplices a piecewise linear control law affine in each simplex is then constructed

continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems invariant pairs have been proposed as a numerically robust means to represent and compute several eigenvalues along with the corresponding generalized eigenvectors for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter in this work we consider nonlinear eigenvalue problems that depend on an additional parameter and our interest is to track several eigenvalues as this parameter varies based on the concept of invariant pairs a theoretically sound and reliable numerical continuation procedure is developed particular attention is paid to the situation when the procedure approaches a singularity that is when eigenvalues included in the invariant pair collide with other eigenvalues for the real generic case it is proven that such a singularity only occurs when two eigenvalues collide on the real axis it is shown how this situation can be handled numerically by an appropriate expansion of the invariant pair the viability of our continuation procedure is illustrated by a numerical example

computing a alpha log a and related matrix functions by contour integrals new methods are proposed for the numerical evaluation of f mathbf a or f mathbf a b where f mathbf a is a function such as mathbf a 1 2 or log mathbf a with singularities in infty 0 and mathbf a is a matrix with eigenvalues on or near 0 infty the methods are based on combining contour integrals evaluated by the periodic trapezoid rule with conformal maps involving jacobi elliptic functions the convergence is geometric so that the computation of f mathbf a b is typically reduced to one or two dozen linear system solves which can be carried out in parallel

computing the common zeros of two bivariate functions via bezout resultants the common zeros of two bivariate functions can be computed by finding the common zeros of their polynomial interpolants expressed in a tensor chebyshev basis from here we develop a bivariate rootfinding algorithm based on the hidden variable resultant method and bezout matrices with polynomial entries using techniques including domain subdivision bezoutian regularization and local refinement we are able to reliably and accurately compute the simple common zeros of two smooth functions with polynomial interpolants of very high degree ge 1 000 1 000 we analyze the resultant method and its conditioning by noting that the bezout matrices are matrix polynomials two implementations are available one on the matlab central file exchange and another in the roots command in chebfun2 that is adapted to suit chebfun s methodology

an accurate and efficient acoustic eigensolver based on a fast multipole bem and a contour integral method an accurate numerical solver is developed in this paper for eigenproblems governed by the helmholtz equation and formulated through the boundary element method a contour integral method is used to convert the nonlinear eigenproblem into an ordinary eigenproblem so that eigenvalues can be extracted accurately by solving a set of standard boundary element systems of equations in order to accelerate the solution procedure the parameters affecting the accuracy and efficiency of the method are studied and two contour paths are compared moreover a wideband fast multipole method is implemented with a block idr s solver to reduce the overall solution cost of the boundary element systems of equations with multiple right hand sides the burton miller formulation is employed to identify the fictitious eigenfrequencies of the interior acoustic problems with multiply connected domains the actual effect of the burton miller formulation on tackling the fictitious eigenfrequency problem is investigated and the optimal choice of the coupling parameter as i k is confirmed through exterior sphere examples furthermore the numerical eigenvalues obtained by the developed method are compared with the results obtained by the finite element method to show the accuracy and efficiency of the developed method

a 2 5d boundary element formulation for modeling damped waves in arbitrary cross section waveguides and cavities a regularized 2 5d boundary element method bem is proposed to predict the dispersion properties of damped stress guided waves in waveguides and cavities of arbitrary cross section the wave attenuation induced by material damping is introduced using linear viscoelastic constitutive relations and described in a spatial manner by the imaginary component of the axial wavenumber the discretized dispersive wave equation results in a nonlinear eigenvalue problem which is solved obtaining complex axial wavenumbers for a fixed frequency using a contour integral algorithm due to the singular characteristics and the multivalued feature of the wave equation the requirement of holomorphicity inside the contour region over the complex wavenumber plane is fulfilled by the introduction of the sommerfeld branch cuts and by the choice of the permissible riemann sheets a post processing analysis is developed for the extraction of the energy velocity of propagative guided waves the reliability of the method is demonstrated by comparing the results obtained for a rail and a bar with square cross section with those obtained from a 2 5d finite element formulation also known in literature as semi analytical finite element safe method next to show the potential of the proposed numerical framework dispersion properties are predicted for surface waves propagating along cylindrical cavities of arbitrary cross section it is demonstrated that the attenuation of surface waves approaches asymptotically the attenuation of rayleigh waves

designing rational filter functions for solving eigenvalue problems by contour integration abstract solving nonlinear eigenvalue problems by contour integration requires an effective discretization for the corresponding contour integrals in this paper it is shown that good rational filter functions can be computed using nonlinear least squares optimization techniques as opposed to designing those functions based on a thorough understanding of complex analysis the conditions that such an effective filter function should satisfy are derived and translated in a nonlinear least squares optimization problem solved by optimization algorithms from tensorlab numerical experiments illustrate the validity of this approach

convex optimization via feedbacks three dynamical systems are associated with a problem of convex optimization in a finite dimensional space for system trajectories x t the ratios x t t are respectively i solution tracking staying within the solution set x 0 ii solution abandoning reaching x 0 as time t goes back to the initial instant and iii solution approaching approaching x 0 as time t goes to infinity the systems represent a closed control system with appropriate feedbacks in typical cases the structure of the trajectories is simple enough for instance for a problem of quadratic programming with linear and box constraints solution approaching dynamics are described by a piecewise linear ode with a finite number of polyhedral domains of linearity finding the order of visiting these domains yields an analytic resolution of the original problem a detailed analysis is given for a particular example a discrete time approach is outlined