Algorithm 1022: Efficient Algorithms for Computing a Rank-Revealing UTV Factorization on Parallel Computing Architectures

DOI10.1145/3507466OpenAlexW4220950446WikidataQ113309846 ScholiaQ113309846MaRDI QIDQ5883714

Nathan Heavner, Francisco D. Igual, Gregorio Quintana-Ortí, Per-Gunnar Martinsson

Publication date: 22 March 2023

Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.05782

zbMATH Keywords

singular value decompositionhigh performancenumerical linear algebrablock algorithmrandomized methodsrandomized SVDrank-revealing matrix factorizationalgorithm-by-blocks

Mathematics Subject Classification ID

Numerical analysis (65-XX)

Related Items (2)

Piecewise DMD for oscillatory and Turing spatio-temporal dynamics ⋮ Algorithm 1022

Uses Software

• FLAME
• LAPACK
• ScaLAPACK
• BLAS
• libflame
• POOCLAPACK
• Algorithm 679
• SuperMatrix
• Algorithm 656
• randUTV

Cites Work

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• Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
• POOCLAPACK
• A randomized algorithm for the decomposition of matrices
• On interpolation and integration in finite-dimensional spaces of bounded functions
• ScaLAPACK: A portable linear algebra library for distributed memory computers -- design issues and performance
• A modified Gram--Schmidt-based downdating technique for ULV decompositions with applications to recursive TLS problems
• Programming matrix algorithms-by-blocks for thread-level parallelism
• A Runtime System for Programming Out-of-Core Matrix Algorithms-by-Tiles on Multithreaded Architectures
• SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS
• A Randomized Algorithm for Principal Component Analysis
• Solving linear-quadratic optimal control problems on parallel computers
• Algorithm 656: an extended set of basic linear algebra subprograms: model implementation and test programs
• A Storage-Efficient $WY$ Representation for Products of Householder Transformations
• LAPACK Users' Guide
• Basic Linear Algebra Subprograms for Fortran Usage
• Downdating the Rank-Revealing URV Decomposition
• ScaLAPACK Users' Guide
• Algorithm 679: A set of level 3 basic linear algebra subprograms: model implementation and test programs
• randUTV
• Updating a Rank-Revealing ULV Decomposition
• FLAME
• Representing linear algebra algorithms in code: the FLAME application program interfaces
• Parallel out-of-core computation and updating of the QR factorization
• Randomized numerical linear algebra: Foundations and algorithms

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