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  1. No Access

    Article

    A continuation method for solving symmetric Toeplitz systems

    A fast algorithm is proposed for solving symmetric Toeplitz systems. This algorithm continuously transforms the identity matrix into the inverse of a given Toeplitz matrix T. The memory requirements for the algor...

    M. Van Barel, Kh. D. Ikramov… in Computational Mathematics and Mathematical… (2008)

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    Article

    A Lanczos–like reduction of symmetric structured matrices to semiseparable form*

    An algorithm that transforms symmetric matrices to similar semiseparable ones was recently proposed [19]. As with the Householder reduction, the latter algorithm works without taking into account the structure...

    N. Mastronardi, M. Schuermans, M. Van Barel, R. Vandebril, S. Van Huffel in CALCOLO (2005)

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    Article

    A bibliography on semiseparable matrices*

    Currently there is a growing interest in semiseparable matrices and generalized semiseparable matrices. To gain an appreciation of the historical evolution of this concept, we present in this paper an extensiv...

    R. Vandebril, M. Van Barel, G. Golub, N. Mastronardi in CALCOLO (2005)

  4. No Access

    Article

    Divide and conquer algorithms for computing the eigendecomposition of symmetric diagonal-plus-semiseparable matrices

    Three fast and stable divide and conquer algorithms to compute the eigendecomposition of symmetric diagonal-plus-semiseparable matrices are considered.

    N. Mastronardi, E. Van Camp, M. Van Barel in Numerical Algorithms (2005)

  5. No Access

    Article

    Solving Toeplitz Least Squares Problems by Means of Newton's Iteration

    We extend the algorithm of [4], based on Newton's iteration and on the concept of ε-displacement rank, to the computation of the generalized inverse A + of an m×n Toeplitz matrix A. We introduce new strategies fo...

    D.A. Bini, G. Codevico, M. Van Barel in Numerical Algorithms (2003)

  6. No Access

    Article

    Error Analysis of a Derivative-Free Algorithm for Computing Zeros of Holomorphic Functions

    We consider the quadrature method developed by Kravanja and Van Barel (Computing 63(1):69–91, 1999) for computing all the zeros of a holomorphic function that lie inside the unit circle. The algorithm uses onl...

    P. Kravanja, T. Sakurai, M. Van Barel in Computing (2003)

  7. No Access

    Article

    On Locating Clusters of Zeros of Analytic Functions

    Given an analytic function f and a Jordan curve γ that does not pass through any zero of f, we consider the problem of computing all the zeros of f that lie inside γ, together with their respective multiplicities...

    P. Kravanja, T. Sakurai, M. Van Barel in BIT Numerical Mathematics (1999)

  8. No Access

    Article

    A Derivative-Free Algorithm for Computing Zeros of Analytic Functions

    Let W be a simply connected region in \(\Bbb C\) , f:W\rightarrow\Bbb C analytic in W and γ a positively oriented Jordan curve in W that does...

    P. Kravanja, M. Van Barel in Computing (1999)

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    Chapter

    Matrix Rational Interpolation with Poles as Interpolation Points

    In this paper, we show the equivalence between matrix rational interpolation problems with poles as interpolation points and no-pole problems. This equivalence provides an effective method for computing matrix...

    M. Van Barel, B. Beckermann, A. Bultheel… in Nonlinear Numerical Methods and Rational A… (1994)

  10. No Access

    Article

    A general module theoretic framework for vector M-Padé and matrix rational interpolation

    A general module theoretic framework is used to solve several classical interpolation problems and generalizations thereof in a unified way. These problems are divided into two main families. The first family ...

    M. Van Barel, A. Bultheel in Numerical Algorithms (1992)