Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications

DOI10.1007/s11075-011-9478-1zbMath1244.65062OpenAlexW2073327480MaRDI QIDQ662894

Katsuhisa Ozaki, Shin'ichi Oishi, Takeshi Ogita, Siegfried Michael Rump

Publication date: 13 February 2012

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-011-9478-1

zbMATH Keywords

floating point arithmeticBLASdot products of vectorserror free matrix multiplicationerror free splitting of floating point numbers

Mathematics Subject Classification ID

Related Items (14)

Tight and efficient enclosure of matrix multiplication by using optimized BLAS ⋮ Iterative refinement for symmetric eigenvalue decomposition ⋮ Fast enclosure for solutions of Sylvester equations ⋮ Floating-point arithmetic ⋮ Iterative refinement of Schur decompositions ⋮ Error‐free transformation of matrix multiplication with a posteriori validation ⋮ Numerical integration as a finite matrix approximation to multiplication operator ⋮ Infinite-precision inner product and sparse matrix-vector multiplication using Ozaki scheme with Dot2 on manycore processors ⋮ Acceleration of iterative refinement for singular value decomposition ⋮ Convergence analysis of an algorithm for accurate inverse Cholesky factorization ⋮ Iterative refinement for singular value decomposition based on matrix multiplication ⋮ Reproducibility strategies for parallel preconditioned conjugate gradient ⋮ Iterative refinement for symmetric eigenvalue decomposition. II. Clustered eigenvalues ⋮ Improvement of error-free splitting for accurate matrix multiplication

Uses Software

• ATLAS
• Matlab
• UMFPACK
• BLAS
• MPFR
• INTLAB
• mctoolbox
• exflib
• XBLAS

Cites Work

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• A floating-point technique for extending the available precision
• Ultimately Fast Accurate Summation
• Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to Nearest
• A Fortran 90-based multiprecision system
• Accurate and Efficient Floating Point Summation
• Accuracy and Stability of Numerical Algorithms
• Accurate Floating-Point Summation Part I: Faithful Rounding
• Design, implementation and testing of extended and mixed precision BLAS
• Accurate Sum and Dot Product
• Automated empirical optimizations of software and the ATLAS project

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