When is the Adjoint of a Matrix a Low Degree Rational Function in the Matrix?

DOI10.1137/060675538zbMath1160.15013OpenAlexW2043921931MaRDI QIDQ3537442

Jörg Liesen

Publication date: 6 November 2008

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://depositonce.tu-berlin.de//handle/11303/7290

zbMATH Keywords

rational interpolationinner productKrylov subspace methodsnormal matricesHermitian positive definite matrixshort recurrencesrepresentation of matrix adjoints

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Iterative numerical methods for linear systems (65F10) Approximation by rational functions (41A20) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Interpolation in approximation theory (41A05) Canonical forms, reductions, classification (15A21)

Related Items (4)

A note on the maximum number of zeros of \(r(z) - \overline{z}\) ⋮ A flexible short recurrence Krylov subspace method for matrices arising in the time integration of port-Hamiltonian systems and ODEs/DAEs with a dissipative Hamiltonian ⋮ On an Economic Arnoldi Method for $BML$-Matrices ⋮ Perturbing rational harmonic functions by poles

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