The design of a parallel dense linear algebra software library: Reduction to Hessenberg, tridiagonal, and bidiagonal form

DOI10.1007/BF02140776zbMath0839.65050OpenAlexW1989396323MaRDI QIDQ1904151

Jaeyoung Choi, Jack J. Dongarra, David W. Walker

Publication date: 16 June 1996

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

Full work available at URL: https://doi.org/10.1007/bf02140776

zbMATH Keywords

performancescalabilitytridiagonal matrixHessenberg matrixeigenproblemsbidiagonal matrixsoftware libraryreduction to normal formdense linear algebra computationsScalable LAPACK

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of matrix norms, conditioning, scaling (65F35) Complexity and performance of numerical algorithms (65Y20) Packaged methods for numerical algorithms (65Y15) Canonical forms, reductions, classification (15A21) Conditioning of matrices (15A12)

Related Items

The Singular Value Decomposition: Anatomy of Optimizing an Algorithm for Extreme Scale, Parallel two-stage reduction to Hessenberg form using dynamic scheduling on shared-memory architectures, An Input/Output Efficient Algorithm for Hessenberg Reduction, Diagonalization of complex symmetric matrices: generalized Householder reflections, iterative deflation and implicit shifts

Uses Software

• LAPACK
• ScaLAPACK
• CLAPACK
• BLAS
• Netlib

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Reduction to condensed form for the eigenvalue problem on distributed memory architectures
• Block reduction of matrices to condensed forms for eigenvalue computations
• The WY Representation for Products of Householder Matrices
• An extended set of FORTRAN basic linear algebra subprograms
• A Storage-Efficient $WY$ Representation for Products of Householder Transformations
• Basic Linear Algebra Subprograms for Fortran Usage
• Block-Cyclic Dense Linear Algebra
• A set of level 3 basic linear algebra subprograms
• Software Libraries for Linear Algebra Computations on High Performance Computers