Parallel and Heterogeneous $m$--Hessenberg--Triangular--Triangular Reduction

DOI10.1137/15M1047349zbMath1355.65047OpenAlexW2579503792MaRDI QIDQ2954487

Nela Bosner, Lars Karlsson

Publication date: 13 January 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1047349

zbMATH Keywords

algorithmnumerical examplesGivens rotations\(m\)-Hessenberg-triangular-triangular formmatrix-matrix multiplicationheterogeneous CPU/GPU implementationsolving shifted linear systems

Mathematics Subject Classification ID

Direct numerical methods for linear systems and matrix inversion (65F05) Canonical forms, reductions, classification (15A21)

Related Items (1)

Parallel reduction of four matrices to condensed form for a generalized matrix eigenvalue algorithm

Uses Software

• LAPACK
• SLICOT
• BLAS
• CUBLAS

Cites Work

• Accelerating the reduction to upper Hessenberg, tridiagonal, and bidiagonal forms through hybrid GPU-based computing
• Efficient algorithm for simultaneous reduction to the \(m\)-Hessenberg-triangular-triangular form
• Blocked algorithms for the reduction to Hessenberg-triangular form revisited
• Recycling BiCG with an Application to Model Reduction
• Efficient generalized Hessenberg form and applications
• $\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
• LAPACK Users' Guide
• Properties of numerical algorithms related to computing controllability
• An algorithm for pole assignment of time invariant linear systems†
• Using Level 3 BLAS in Rotation-Based Algorithms

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