Fast matrix multiplication is stable

DOI10.1007/s00211-007-0061-6zbMath1134.65030arXivmath/0603207OpenAlexW2147348850MaRDI QIDQ879926

James W. Demmel, Ioana Dumitriu, O. V. Holtz, Robert D. Kleinberg

Publication date: 10 May 2007

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603207

zbMATH Keywords

forward error analysisMatrix multiplicationgroup-theoretic algorithmsnumerically stable algorithms

Mathematics Subject Classification ID

Roundoff error (65G50)

Related Items

Fast matrix multiplication by using color algebras, Pseudospectral shattering, the sign function, and diagonalization in nearly matrix multiplication time, Fast structured matrix computations: tensor rank and Cohn-Umans method, Fast matrix multiplication and its algebraic neighbourhood, Unnamed Item, Fast linear algebra is stable, Strassen's Algorithm for Tensor Contraction, Communication lower bounds and optimal algorithms for numerical linear algebra, Improving the Numerical Stability of Fast Matrix Multiplication, Unnamed Item

Uses Software

• LAPACK
• ScaLAPACK
• CLAPACK
• mctoolbox

Cites Work

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• Fast multiplication of large numbers
• LAPACK Users' Guide
• Computational Complexity and Numerical Stability
• ScaLAPACK Users' Guide
• Exploiting fast matrix multiplication within the level 3 BLAS
• Stability of block algorithms with fast level-3 BLAS
• On the Complexity of Matrix Product
• Accuracy and Stability of Numerical Algorithms