Accelerating the reduction to upper Hessenberg, tridiagonal, and bidiagonal forms through hybrid GPU-based computing

DOI10.1016/j.parco.2010.06.001zbMath1214.65020OpenAlexW2125960020MaRDI QIDQ608851

Rajib Nath, Stanimire Z. Tomov, Jack J. Dongarra

Publication date: 26 November 2010

Published in: Parallel Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.parco.2010.06.001

zbMATH Keywords

GPUsbidiagonalizationdense linear algebraHessenberg reductionhybrid computingtridiagonalizationtwo-sided factorizations

Mathematics Subject Classification ID

Numerical algorithms for specific classes of architectures (65Y10)

Related Items

Algorithm 1019: A Task-based Multi-shift QR/QZ Algorithm with Aggressive Early Deflation, The Singular Value Decomposition: Anatomy of Optimizing an Algorithm for Extreme Scale, Parallel Solver for Shifted Systems in a Hybrid CPU--GPU Framework, Parallel and Heterogeneous $m$--Hessenberg--Triangular--Triangular Reduction, Numerical algorithms for the determinant evaluation of general Hessenberg matrices, KBLAS, Algorithm 953, Linear algebra software for large-scale accelerated multicore computing, Parallel two-stage reduction to Hessenberg form using dynamic scheduling on shared-memory architectures, Towards dense linear algebra for hybrid GPU accelerated manycore systems, A Scalable High Performant Cholesky Factorization for Multicore with GPU Accelerators

Uses Software

• LAPACK
• Magma
• CUDA
• MAGMA

Cites Work

• Unnamed Item
• Towards dense linear algebra for hybrid GPU accelerated manycore systems
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• A Scalable High Performant Cholesky Factorization for Multicore with GPU Accelerators
• Minimizing Communication in Numerical Linear Algebra
• The WY Representation for Products of Householder Matrices
• A Storage-Efficient $WY$ Representation for Products of Householder Transformations
• LAPACK Users' Guide
• Using the Hessenberg decomposition in control theory
• Communication-optimal Parallel and Sequential Cholesky Decomposition