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Programming on ENIAC (source: US National Archive)

Green generators for inverses of banded matrices

This is companion software to the manuscript Computation of quasiseparable representations of Green matrices (with Y. Eidelman).
  • Matlab code

    • Rational approximation of ψ1(A)

    Numerical tests for a rational approximation of the reciprocal of the φ1 function applied to a matrix. This is companion software to the manuscript Computing the reciprocal of a φ function by rational approximation (with Y. Eidelman and L. Gemignani).
  • Matlab code

    • Parameter dependent quasiseparable systems

    Fast solution of shifted linear systems, with applications to matrix equations with quasiseparable coefficients and to the computation of functions of quasiseparable matrices. This is companion software to the manuscript Efficient Solution of Parameter Dependent Quasiseparable Systems (with Y. Eidelman and L. Gemignani).
  • Matlab code

    • Structured QR/QZ

    Code for fast computation of eigenvalues of companion matrices using a structured version of the implicit QR method.
    Without compression:
    This is a Fortran 90 implementation of the algorithms described in the paper A Fast Implicit QR Eigenvalue Algorithm for Companion Matrices (with D. A. Bini, Y. Eidelman, L. Gemignani and I. Gohberg, LAA 2010).
  • Single shift
  • Double shift
    • With compression:
    Companion software to the article Implicit QR with Compression (with Y. Eidelman, L. Gemignani and I. Gohberg, Indag. Math. 2012).
  • Matlab code, single shift
  • Fortran 90 code, single shift
  • Matlab code, double shift
    • Structured QZ for companion pencils
    Code for fast computation of generalized eigenvalues of companion pencils. The single-shift version is companion software to the article Implicit QR for companion-like pencils (with Y. Eidelman and L. Gemignani, Math. Comp. 2016). The double-shift version implements the algorithm described in the paper A real QZ algorithm for structured companion pencils (with Y. Eidelman and L. Gemignani, Calcolo 2016).
  • Matlab code, single shift
  • Fortran 90 code, single shift
  • Matlab code, double shift
  • Fortran 90 code, double shift

    • Approximate polynomial GCD

    Matlab code for fast computation of approximate polynomial GCD. This is an implementation of the fast algorithm described in the paper
    A fast algorithm for approximate polynomial gcd based on structured matrix computations (with D.A. Bini, Operator Theory 2010).
  • Fastgcd

    • Multiplication Matrix GCD

    Matlab code for fast implementation of approximate polynomial GCD with one exact polynomial. Companion software to the paper Extended companion matrix for approximate GCD (with O. Ruatta), presented at SNC 2011.
  • MMgcd

    • Condition geodesics in matrix spaces

    Companion software to the paper The condition metric in the space of rectangular full rank matrices (with J.-P. Dedieu, SIMAX 2010).
  • Condition geodesics.This Matlab code allows to compute condition geodesics in the space of real square nonsingular matrices.