K. A. Gallivan, S. Thirumalai, P. Van Dooren, V. Vermaut
In this paper, we present several high performance variants of the classical Schur algorithm to factor various Toeplitz matrices. For positive definite block Toeplitz matrices, we show how hyperbolic...
Model Reduction of Large-Scale Dynamical Systems (2008)
A. Antoulas, D. Sorensen, K. A. Gallivan, P. Van Dooren, A. Grama, A. Sameh
Abstract. Simulation and control are two critical elements of Dynamic Data-Driven Application Systems (DDDAS). Simulation of dynamical systems such as weather phenomena, when augmented with real-time...
Model Reduction of Large-Scale Dynamical Systems (2008)
A. Antoulas, D. Sorensen, K. A. Gallivan, P. Van Dooren, A. Grama, C. Hoffmann, ...
Abstract. Simulation and control are two critical elements of Dynamic Data-Driven Application Systems (DDDAS). Simulation of dynamical systems such as weather phenomena, when augmented with real-time...
Templates for the Solution of Algebraic Eigenvalue Problems: a Practical (2008)
P. A. Absil, R. Sepulchre, P. Van Dooren, R. Mahony, Z. Bai, J. Demmel, ...
[7] W. E. Arnoldi, The principle of minimized iteration in the solution of the matrix eigenproblem, Quart. Appl. Math. 9 (1951), no. 1, 17–29.
Social Leaders in Graphs (2008)
V. Blondel, C. De Kerchove, E. Huens, P. Van Dooren
We introduce the definition of Social Leader that gives a local centrality measure for each node in a graph. A node u is a Social Leader if the number of cycles of length 3 passing through u is...
A. W. Bojanczyk, R. P. Brent, P. Van Dooren
We analyse and compare three algorithms for “downdating ” the Cholesky factorization of a positive definite matrix. Although the algorithms are closely related, their numerical properties differ....
Quotient Iteration for Computing Invariant Subspaces ∗ (2008)
R. Mahony, R. Sepulchre, P. Van Dooren
Abstract. The classical Rayleigh quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQI which...
Direct Method-Based Preconditioners to Solve Regularization Problems in Image Deconvolution (2007)
S. Thirumalai, K. A. Gallivan, P. Van Dooren
In this paper we consider the problem of restoring images that have been blurred by a spatially-invariant point spread function (PSF). This problem is well-studied and in recent years several...
Smoothly Time Varying Systems and Least Squares System Identification (2007)
Michael Stewart, P. Van Dooren
This paper considers the significance of smoothness from a somewhat broader perspective. Three issues are involved. The first is the ability of the identification algorithm to track a smooth model...
Algorithms for rank-deficient and ill-conditioned Toeplitz least-squares and QR factorization (2007)
Thirumalai Gallivan, S. Thirumalai, K. A. Gallivan, P. Van Dooren
In this paper we present two algorithms - one to compute the QR factorization of nearly rank-deficient Toeplitz and block Toeplitz matrices and the other to compute the solution of a severely...
1 Introduction Model reduction via tangential interpolation (2007)
Although most of the theory presented in this paper holds for both continuous-time and
Quotient Iteration for Computing Invariant Subspaces # (2007)
R. Mahony, R. Sepulchre, P. Van Dooren
Abstract. The classical Rayleigh quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQI which...
Centre for Engineering Systems and Applied Mechanics (2007)
Abstract: We present an up-to-date survey of numerical methods for the analysis and design of linear discrete-time periodic systems. The basic tool is the periodic Schur form and its variants, for...
FAST IMPLEMENTATION OF THE QR FACTORIZATION IN SUBSPACE IDENTIFICATION (2007)
N. Mastronardi, P. Van Dooren, S. Van Huffel
Two recent approaches [4, 14] in subspace identification problems require the computation of the Ê factor of the ÉÊ factorization of a block–Hankel matrix À, which, in general has a huge number...
A Grassmann-Rayleigh Quotient Iteration for Computing Invariant Subspaces (2007)
R. Mahonyx, R. Sepulchrez, P. Van Dooren
The classical Rayleigh Quotient Iteration (RQI) computes a 1-dimensional invariant subspace of a symmetric matrix A with cubic convergence. We propose a generalization of the RQI which computes a...
Dooren, Real and complex stability radii of polynomial matrices, submitted (2007)
Y. Genin, R. Stefan, P. Van Dooren
In this paper, analytic expressions are derived for the complex and real stability radii of non-monic polynomial matrices with respect to an arbitrary stability region of the complex plane. Numerical...
Y. Genin, I. Ipsen, R. Stefan, P. Van Dooren
radius and optimal scaling of discrete-time periodic systems
Y. Genin, Y. Hachez, Yu. Nesterov, P. Van Dooren
Positive polynomial matrices play a fundamental role in systems and control theory: they represent e.g. spectral density functions of stochastic processes and show up in spectral factorizations,...
K. Gallivan, X. Rao, P. Van Dooren
equation In this paper we discuss the convergence of a stabilization algorithm based on a singular version of the Discrete Riccati Difference Equation. This method is particularly appealing for large...
Dooren, Model reduction of second order systems (2005)
Y. Chahlaoui, K. A. Gallivan, P. Van Dooren
In this chapter, the problem of constructing a reduced order system while preserving the second order structure of the original system is discussed. After a brief introduction on second order systems...
Cubically convergent iterations for invariant subspace computation (2004)
R. Sepulchre, P. Van Dooren, R. Mahony
Abstract. We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of R n and converges locally cubically to the invariant subspaces of a symmetric matrix. This...
Model reduction of MIMO systems via tangential interpolation (2004)
K. Gallivan, A. Vandendorpe, P. Van Dooren
Abstract. In this paper, we address the problem of constructing a reduced order system of minimal McMillan degree that satisfies a set of tangential interpolation conditions with respect to the...
Computing the zeros of periodic descriptor systems (2003)
In this paper, we give a numerically reliable algorithm to compute the zeros of a periodic descriptor system. The algorithm is a variant of the staircase algorithm applied to the system pencil of an...
Abstract ARTICLE IN PRESS Linear Algebra and its Applications xx (2004) xxx–xxx (2003)
Y. Chahlaoui, D. Lemonnier, P. Van Dooren
www.elsevier.com/locate/laa Second-order balanced truncation
Optimization problems over positive pseudo-polynomial matrices (2003)
Y. Genin, Y. Hachez, Yu. Nesterov, P. Van Dooren
The Nesterov characterizations of positive pseudo-polynomials on the real line, the imaginary and the unit circle are extended to the matrix case. With the help of these characterizations, a class of...
Elliptic and hyperbolic quadratic eigenvalue problems and associated distance problems (2002)
Two important classes of quadratic eigenvalue problems are composed of elliptic and hyperbolic problems. In [Linear Algebra Appl., 351–352 (2002) 455], the distance to the nearest non-hyperbolic or...
Dooren, A Grassmann-Rayleigh quotient iteration for computing invariant subspaces (2002)
R. Mahony, R. Sepulchre, P. Van Dooren
y{
Positivity and linear matrix inequalities (2002)
Y. Genin, Y. Hachez, Yu. Nesterov, P. Van Dooren, S. Xu
In this paper we rst recall the general theory of Popov realizations of parahermitian transfer functions in the context of generalized state space systems. We then use this general framework to...
X. Rao, K. Gallivan, P. Van Dooren
difference equation In this paper we discuss the convergence of a stabilization algorithm based on a singular version of the Discrete Riccati Difference Equation. This method is particularly...
Computational Methods for Periodic Systems - An Overview (2001)
We present an up-to-date survey of numerical methods for the analysis and design of linear discrete-time periodic systems. The basic tool is the periodic Schur form and its variants, for which a...
Optimization over Positive Polynomial Matrices (2000)
Y. Genin, Yu. Nesterov, P. Van Dooren
Positive polynomial matrices play a fundamental role in systems and control theory. We give here a simplified proof of the fact that the convex set of positive polynomial matrices can be...
Efficient stabilization of large scale dynamical systems (2000)
X. Rao, K. A. Gallivan, P. Van Dooren
In this paper we discuss the stabilization of large scale linear time invariant dynamical systems via feedback. An overview of efficient schemes based on the Discrete Riccati Difference Equation are...
Dooren, Stabilization of Large Scale Dynamical Systems (2000)
X. Rao, K. A. Gallivan, P. Van Dooren
In this paper we discuss the stabilization of large scale linear time invariant dynamical systems via feedback. Efficient schemes based on the Discrete Riccati Difference Equation are presented. The...
Recursive calculation of dominant singular subspaces (1999)
Y. Chahlaoui, K. Gallivan, P. Van Dooren
Abstract. In this paper we show how to compute recursively an approximation of the left and right dominant singular subspaces of a given matrix. In order to perform as few as possible operations on...
Least Squares Support Vector Machine Classifiers: a Large Scale Algorithm (1999)
L. Lukas, P. Van Dooren, B. De Moor, J. Vandewalle
Support vector machines (SVM's) have been introduced in literature as a method for pattern recognition and function estimation, within the framework of statistical learning theory and structural...
A rational Lanczos algorithm for model reduction (1996)
K. Gallivan, E. Grimme, P. Van Dooren
This paper presents a model reduction method for large-scale linear systems that is based on a Lanczos-type approach. A variant of the nonsymmetric Lanczos method, rational Lanczos, is shown to yield...
Model reduction of state space systems via an implicitly restarted Lanczos method (1996)
Grimme Coordinated, E. J. Grimme, E. J. Grimme, D. C. Sorensen, D. C. Sorensen, P. Van Dooren, ...
The nonsymmetric Lanczos method has recently received significant attention as a model reduction technique for large-scale systems. Unfortunately, the Lanczos method may produce an unstable partial...
High Performance Algorithms for Toeplitz and block Toeplitz matrices (1996)
K. A. Gallivan, S. Thirumalai, P. Van Dooren, V. Vermaut, P. Van, Dooren V. Vermaut
this paper we discuss several high performance variants of the classical Schur algorithm algorithms to factor symmetric block Toeplitz matrices. Specifically we discuss routines to factor symmetric...
A Rational Lanczos Algorithm for Model Reduction (1996)
K. Gallivan, E. Grimme, P. Van Dooren
This paper presents a model reduction method for large-scale linear systems that is based on a Lanczos-type approach. A variant of the nonsymmetric Lanczos method, rational Lanczos, is shown to yield...
Model reduction of state space systems via an implicitly restarted Lanczos method (1996)
E.J. Grimme, D. C. Sorensen, P. Van Dooren
The nonsymmetric Lanczos method has recently received significant attention as a model reduction technique for large-scale systems. Unfortunately, the Lanczos method may produce an unstable partial...
High Performance Algorithms for Toeplitz and block Toeplitz matrices (1996)
K. A. Gallivan, S. Thirumalai, P. Van Dooren, V. Vermaut, P. Van, Dooren V. Vermaut
this paper we discuss several high performance variants of the classical Schur algorithm algorithms to factor symmetric block Toeplitz matrices. Specifically we discuss routines to factor symmetric...
A Rational Lanczos Algorithm for Model Reduction (1996)
K. Gallivan, E. Grimme, P. Van Dooren
This paper presents a model reduction method for large-scale linear systems that is based on a Lanczos-type approach. A variant of the nonsymmetric Lanczos method, rational Lanczos, is shown to yield...
On some modifications of the Lanczos algorithm and the relation with Padé approximations (1995)
K. Gallivan, E. Grimme, D. Sorensen, P. Van Dooren
In this paper we try to show the relations between the Lanczos algorithm and Pad'e approximations as used e.g. in identification and model reduction of dynamical systems. 1 1 Introduction For...
On some modifications of the Lanczos algorithm and the relation with Padé approximations (1995)
K. Gallivan, E. Grimme, D. Sorensen, P. Van Dooren
In this paper we try to show the relations between the Lanczos algorithm and Pad'e approximations as used e.g. in identification and model reduction of dynamical systems. We also explore the use...
Recursive All Pass Realizations Subject to Tangential Constraints (1995)
Given d complex points i and associated directions (of C n ) z i , we develop a recursive algorithm for obtaining a " I 2 \Sigma # -unitary realization fA; B; C; Dg of a \Sigma-unitary transfer...
Asymptotic waveform evaluation via a Lanczos method (1994)
K. Gallivan, E. Grimme, P. Van Dooren
Abstract-In this paper we show that the two-sided Lanczos procedure combined with implicit restarts, offers significant advantages over Pad6 approximations used typically for model reduction in...
Placing zeroes and the Kronecker canonical form (1994)
Given a linear time-invariant control system, it is well known that the transmission zeroes are the generalized eigenvalues of a matrix pencil. Adding outputs to place additional zeroes is equivalent...
Padé Approximation Of Large-Scale Dynamic Systems With Lanczos Methods (1994)
K. Gallivan, E. Grimme, P. Van Dooren
The utility of Lanczos methods for the approximation of large-scale dynamical systems is considered. In particular, it is shown that the Lanczos method is a technique for yielding Pad'e...
Placing Zeroes And The Kronecker Canonical Form (1994)
Given a linear time-invariant control system, it is well known that the transmission zeroes are the generalized eigenvalues of a matrix pencil. Adding outputs to place additional zeroes is equivalent...
Asymptotic Waveform Evaluation via a Lanczos Method (1994)
K. Gallivan, E. Grimme, P. Van Dooren
In this paper we show that the two-sided Lanczos procedure combined with implicit restarts offers significant advantages over Pad'e approximations used typically for model reduction in circuit...
Periodic Schur form and some matrix equations (1993)
We propose an elegant and conceptually simple method for computing the periodic solution of three classes of periodic matrix equations --- Riccati, Lyapunov and Sylvester. Such equations arise...