Blocked algorithms for the reduction to Hessenberg-triangular form revisited

DOI10.1007/s10543-008-0180-1zbMath1157.65348OpenAlexW2107864772MaRDI QIDQ960033

Daniel Kressner, Gregorio Quintana-Ortí, Bo Kågström, Enrique S. Quintana-Ortí

Publication date: 16 December 2008

Published in: BIT (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11850/12960

zbMATH Keywords

high-performance computingorthogonal transformationsQZ algorithmgeneralized eigenvalue problemslevel 3 BLASblocked algorithmsHessenberg-triangular form

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Complexity and performance of numerical algorithms (65Y20)

Related Items

A Householder-Based Algorithm for Hessenberg-Triangular Reduction, Parallel and Heterogeneous $m$--Hessenberg--Triangular--Triangular Reduction, Increasing data locality and introducing level-3 BLAS in the neville elimination, Simultaneous band reduction of two symmetric matrices, Distributed One-Stage Hessenberg-Triangular Reduction with Wavefront Scheduling, Parallel reduction of four matrices to condensed form for a generalized matrix eigenvalue algorithm, Algorithm 953, Unnamed Item, Restructuring the Tridiagonal and Bidiagonal QR Algorithms for Performance, Parallel two-stage reduction to Hessenberg form using dynamic scheduling on shared-memory architectures, Efficient algorithm for simultaneous reduction to the \(m\)-Hessenberg-triangular-triangular form, Algorithms for Hessenberg-Triangular Reduction of Fiedler Linearization of Matrix Polynomials, Parallel codes for computing the numerical rank, Fast Hessenberg Reduction of Some Rank Structured Matrices

Uses Software

• LAPACK
• GEMM
• CLAPACK
• BLAS

Cites Work

• Parallel QR decomposition of a rectangular matrix
• On a modification of the QZ algorithm with fast Givens rotations
• Block reduction of matrices to condensed forms for eigenvalue computations
• An alternative Givens ordering
• The Multishift QR Algorithm. Part I: Maintaining Well-Focused Shifts and Level 3 Performance
• Improving the performance of reduction to Hessenberg form
• Anatomy of high-performance matrix multiplication
• The WY Representation for Products of Householder Matrices
• A Storage-Efficient $WY$ Representation for Products of Householder Transformations
• LAPACK Users' Guide
• GEMM-based level 3 BLAS
• Using Level 3 BLAS in Rotation-Based Algorithms
• A framework for symmetric band reduction
• Blocked algorithms and software for reduction of a regular matrix pair to generalized Schur form
• Multishift Variants of the QZ Algorithm with Aggressive Early Deflation
• An Algorithm for Generalized Matrix Eigenvalue Problems
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