Block reduction of matrices to condensed forms for eigenvalue computations

DOI10.1016/0377-0427(89)90367-1zbMath0679.65025OpenAlexW2164895445MaRDI QIDQ1822900

Jack J. Dongarra, Sven J. Hammarling, Danny C. Sorensen

Publication date: 1989

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(89)90367-1

zbMATH Keywords

singular value decompositioneigenvaluesblock algorithmsHouseholder transformationsdivide and conquer techniquereduction to tridiagonal formreduction to Hessenberg formparallel-vector processorsreductions to condensed forms

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Parallel numerical computation (65Y05)

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Advantages of modal decomposition for efficient scaling of parallel FDTD computations, The Singular Value Decomposition: Anatomy of Optimizing an Algorithm for Extreme Scale, The design of a parallel dense linear algebra software library: Reduction to Hessenberg, tridiagonal, and bidiagonal form, Accelerating the reduction to upper Hessenberg, tridiagonal, and bidiagonal forms through hybrid GPU-based computing, A Householder-Based Algorithm for Hessenberg-Triangular Reduction, A mathematical biography of Danny C. Sorensen, Parallel block tridiagonalization of real symmetric matrices, A case against a divide and conquer approach to the nonsymmetric eigenvalue problem, Unnamed Item, Blocked algorithms for the reduction to Hessenberg-triangular form revisited, Linear algebra software for large-scale accelerated multicore computing, Adaptive blocking in the QR factorization, Parallel two-stage reduction to Hessenberg form using dynamic scheduling on shared-memory architectures, Parallel algorithms for reduction of a general matrix to upper Hessenberg form on a shared memory multiprocessor, An Input/Output Efficient Algorithm for Hessenberg Reduction, A Massively Parallel Dense Symmetric Eigensolver with Communication Splitting Multicasting Algorithm, Parallel algorithms for reduction of a symmetric matrix to tridiagonal form on a shared memory multiprocessor

Uses Software

• BLAS

Cites Work

• Squeezing the most out of eigenvalue solvers on high-performance computers
• Linear algebra on high performance computers
• Implementing Dense Linear Algebra Algorithms Using Multitasking on the CRAY X-MP-4 (or Approaching the Gigaflop)
• A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem
• The WY Representation for Products of Householder Matrices
• A set of level 3 basic linear algebra subprograms
• Analysis of Algorithms for Reflections in Bisectors