Vectorization of a Thread-Parallel Jacobi Singular Value Decomposition Method

DOI10.1137/22m1478847zbMath1523.65035arXiv2202.08361OpenAlexW4379162803MaRDI QIDQ6097868

Vedran Novaković

Publication date: 7 June 2023

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

Full work available at URL: https://arxiv.org/abs/2202.08361

zbMATH Keywords

singular value decompositionSIMD vectorizationbatched eigendecomposition of Hermitian matrices of order twoparallel one-sided Jacobi-type SVD method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Parallel numerical computation (65Y05) Orthogonalization in numerical linear algebra (65F25) Numerical algorithms for specific classes of architectures (65Y10)

Cites Work

• A GPU-based hyperbolic SVD algorithm
• Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices
• Block recursive algorithm to generate Jacobi-sets
• A Kogbetliantz-type algorithm for the hyperbolic SVD
• Solution of linear equations by diagonalization of coefficients matrix
• The QR Transformation A Unitary Analogue to the LR Transformation--Part 1
• A Hierarchically Blocked Jacobi SVD Algorithm for Single and Multiple Graphics Processing Units
• New Fast and Accurate Jacobi SVD Algorithm. I
• New Fast and Accurate Jacobi SVD Algorithm. II
• A One-Sided Jacobi Algorithm for Computing the Singular Value Decomposition on a Vector Computer
• LAPACK Users' Guide
• Jacobi’s Method is More Accurate than QR
• Implementation of Jacobi Rotations for Accurate Singular Value Computation in Floating Point Arithmetic
• Implementing High-performance Complex Matrix Multiplication via the 3m and 4m Methods
• Algorithm 978
• New Dynamic Orderings for the Parallel One–Sided Block-Jacobi SVD Algorithm
• Orthogonal Eigenvectors and Relative Gaps
• On the Convergence of the Jacobi Method for Arbitrary Orderings
• On the convergence of complex Jacobi methods
• A Set of Batched Basic Linear Algebra Subprograms and LAPACK Routines
• Batched Computation of the Singular Value Decompositions of Order Two by the AVX-512 Vectorization
• The LAPW Method with Eigendecomposition Based on the Hari--Zimmermann Generalized Hyperbolic SVD
• Linear algebra software for large-scale accelerated multicore computing
• Dynamic ordering for a parallel block-Jacobi SVD algorithm

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