On the Description and Stability of Orthogonal Transformations of Rank Structured Matrices

DOI10.1137/15M1041900zbMath1349.65105MaRDI QIDQ2834688

Michael Stewart

Publication date: 23 November 2016

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

zbMATH Keywords

fast algorithmsbackward errorplane rotationquasiseparable matrixrank structured matrix

Mathematics Subject Classification ID

Roundoff error (65G50) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (1)

Structured generalized eigenvalue condition numbers for parameterized quasiseparable matrices

Uses Software

• mctoolbox

Cites Work

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• Implicit double shift \(QR\)-algorithm for companion matrices
• A multiple shift \(QR\)-step for structured rank matrices
• Separable type representations of matrices and fast algorithms. Volume 2. Eigenvalue method
• Eigenvalue computation for unitary rank structured matrices
• The QR iteration method for Hermitian quasiseparable matrices of an arbitrary order
• Superfast and Stable Structured Solvers for Toeplitz Least Squares via Randomized Sampling
• A Hessenberg Reduction Algorithm for Rank Structured Matrices
• A Givens-Weight Representation for Rank Structured Matrices
• A QR-Based Solver for Rank Structured Matrices
• Accuracy and Stability of Numerical Algorithms
• Fast and Backward Stable Computation of Roots of Polynomials
• Fast QR Eigenvalue Algorithms for Hessenberg Matrices Which Are Rank‐One Perturbations of Unitary Matrices
• Stability of QR-based fast system solvers for a subclass of quasiseparable rank one matrices
• Nested Product Decomposition of Quasiseparable Matrices

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