Efficient eigenvalue computation for quasiseparable Hermitian matrices under low rank perturbations

DOI10.1007/s11075-008-9172-0zbMath1139.65026OpenAlexW2165797890MaRDI QIDQ2483050

Israel Gohberg, Luca Gemignani, Yu.S.Eidel'man

Publication date: 5 May 2008

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-008-9172-0

zbMATH Keywords

complexitynumerical experimentsHermitian matrixquasiseparable matricesHessenberg reductionQR eigenvalue algorithm

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Complexity and performance of numerical algorithms (65Y20)

Related Items (11)

Structured backward errors in linearizations ⋮ A fast implicit QR eigenvalue algorithm for companion matrices ⋮ Unnamed Item ⋮ A condensed representation of almost normal matrices ⋮ Block tridiagonal reduction of perturbed normal and rank structured matrices ⋮ Fast computation of eigenvalues of companion, comrade, and related matrices ⋮ Implicit QR for companion-like pencils ⋮ A CMV-Based Eigensolver for Companion Matrices ⋮ Rank-Structured QR for Chebyshev Rootfinding ⋮ Fast and Backward Stable Computation of Roots of Polynomials ⋮ Fast Hessenberg Reduction of Some Rank Structured Matrices

Uses Software

• LAPACK
• CLAPACK
• mctoolbox

Cites Work

• Unnamed Item
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• On the fast reduction of a quasiseparable matrix to Hessenberg and tridiagonal forms
• Inverse power and Durand-Kerner iterations for univariate polynomial root-finding
• Fast and stable eigendecomposition of symmetric banded plus semi-separable matrices
• Fast and stable QR eigenvalue algorithms for generalized companion matrices and secular equations
• Effects of a parameter on a nonsymmetric algebraic Riccati equation
• The QR iteration method for Hermitian quasiseparable matrices of an arbitrary order
• The QR Transformation A Unitary Analogue to the LR Transformation--Part 1
• Chasing Algorithms for the Eigenvalue Problem
• An implicit QR algorithm for symmetric semiseparable matrices
• LAPACK Users' Guide
• Nonsymmetric Algebraic Riccati Equations and Hamiltonian-like Matrices
• Accuracy and Stability of Numerical Algorithms

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