Blocked algorithms and software for reduction of a regular matrix pair to generalized Schur form

DOI10.1145/332242.332244zbMath0962.65041OpenAlexW2166002122WikidataQ113310004 ScholiaQ113310004MaRDI QIDQ4518220

Krister Dackland, Bo Kågström

Publication date: 20 November 2000

Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1145/332242.332244

zbMATH Keywords

performancegeneralized eigenvalue problemparallelizationmemory hierarchyGivens rotationsLAPACKgeneralized Schur formblocked algorithmsHessenberg-triangular reduction\(QZ\)-algorithmreduction of a matrix pair to Schur form

Mathematics Subject Classification ID

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

Related Items

Generalized subspace iteration method for solving matrix pair eigenproblem ⋮ Simultaneous band reduction of two symmetric matrices ⋮ Distributed One-Stage Hessenberg-Triangular Reduction with Wavefront Scheduling ⋮ Efficient Reduction of Banded Hermitian Positive Definite Generalized Eigenvalue Problems to Banded Standard Eigenvalue Problems ⋮ Blocked algorithms for the reduction to Hessenberg-triangular form revisited ⋮ Parallel two-stage reduction to Hessenberg form using dynamic scheduling on shared-memory architectures ⋮ RECSY and SCASY Library Software: Recursive Blocked and Parallel Algorithms for Sylvester-Type Matrix Equations with Some Applications ⋮ Efficient algorithm for simultaneous reduction to the \(m\)-Hessenberg-triangular-triangular form ⋮ Algorithms for Hessenberg-Triangular Reduction of Fiedler Linearization of Matrix Polynomials

Uses Software

• LAPACK
• ScaLAPACK
• GEMM
• Algorithm 679