A Multishift, Multipole Rational QZ Method with Aggressive Early Deflation

DOI10.1137/19M1249631zbMath1467.65032arXiv1902.10954MaRDI QIDQ4994439

Karl Meerbergen, Thijs Steel, Daan Camps, Raf Vandebril

Publication date: 18 June 2021

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

Full work available at URL: https://arxiv.org/abs/1902.10954

zbMATH Keywords

generalized eigenvaluesrational KrylovFortran implementationaggressive early deflationmultishiftrational QZ

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (3)

Algorithm 1019: A Task-based Multi-shift QR/QZ Algorithm with Aggressive Early Deflation ⋮ Swapping \(2 \times 2\) blocks in the Schur and generalized Schur form ⋮ Unnamed Item

Uses Software

• BLAS
• eigs
• MatrixMarket
• IFISS
• MKL
• IRAM

Cites Work

• Computing eigenspaces with specified eigenvalues of a regular matrix pair \((A,B)\) and condition estimation: Theory, algorithms and software
• The transmission of shifts and shift blurring in the QR algorithm
• Swapping \(2 \times 2\) blocks in the Schur and generalized Schur form
• Pole-swapping algorithms for alternating and palindromic eigenvalue problems
• On pole-swapping algorithms for the eigenvalue problem
• The Multishift QR Algorithm. Part I: Maintaining Well-Focused Shifts and Level 3 Performance
• The Multishift QR Algorithm. Part II: Aggressive Early Deflation
• A Parallel QZ Algorithm for Distributed Memory HPC Systems
• Algorithm 866
• A Generalized Eigenvalue Approach for Solving Riccati Equations
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• IFISS: A Computational Laboratory for Investigating Incompressible Flow Problems
• A Rational QZ Method
• Generalized Rational Krylov Decompositions with an Application to Rational Approximation
• The Matrix Eigenvalue Problem
• Multishift Variants of the QZ Algorithm with Aggressive Early Deflation
• An updated set of basic linear algebra subprograms (BLAS)
• Optimally packed chains of bulges in multishift QR algorithms
• An Algorithm for Generalized Matrix Eigenvalue Problems

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