AB-algorithm and its modifications for the spectral problems of linear pencils of matrices

DOI10.1007/BF01390177zbMath0542.65020MaRDI QIDQ795472

V. N. Kublanovskaya

Publication date: 1984

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132905

zbMATH Keywords

polynomial matricesreductionregular pencilinfinite eigenvaluesAB-algorithmincorporation of shiftsJordan canonical basisquasitriangular form

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Canonical forms, reductions, classification (15A21)

Related Items (17)

A new look at pencils of matrix valued functions ⋮ Spectral division methods for block generalized Schur decompositions ⋮ An improved algorithm for the computation of Kronecker's canonical form of a singular pencil ⋮ Evaluating products of matrix pencils and collapsing matrix products ⋮ To the memory of V. N. Kublanovskaya ⋮ Solution of systems of nonlinear algebraic equations in three variables. Methods and algorithms. III ⋮ Where is the nearest non-regular pencil? ⋮ Methods and algorithms of solving spectral problems for polynomial and rational matrices ⋮ The Bauer-type factorization of matrix polynomials revisited and extended ⋮ To solving the eigenvalue problem for polynomial matrices of general form ⋮ Duality of matrix pencils, Wong chains and linearizations ⋮ An arithmetic for matrix pencils: theory and new algorithms ⋮ A quadratically convergent QR-like method without shifts for the Hermitian eigenvalue problem ⋮ Parallel algorithm for solving some spectral problems of linear algebra ⋮ Root polynomials and their role in the theory of matrix polynomials ⋮ Numerical methods and questions in the organization of calculus. XII. Transl. from the Russian ⋮ On reducing infinite eigenvalues of regular pencils by a nonequivalence transformation

Cites Work

• Singular value decomposition and least squares solutions
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