Tight and efficient enclosure of matrix multiplication by using optimized BLAS

DOI10.1002/nla.724zbMath1249.65098OpenAlexW2003815079MaRDI QIDQ2889382

Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi Oishi

Publication date: 7 June 2012

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nla.724

zbMATH Keywords

algorithmsnumerical examplesinterval arithmeticinterval matrixmatrix multiplicationverified numerical computation

Mathematics Subject Classification ID

Related Items (5)

Fast enclosure for solutions of Sylvester equations ⋮ Error‐free transformation of matrix multiplication with a posteriori validation ⋮ Verified error bounds for solutions of Sylvester matrix equations ⋮ A fast and efficient algorithm for solving ill-conditioned linear systems ⋮ Improvement of error-free splitting for accurate matrix multiplication

Uses Software

• BLAS
• INTLAB
• mctoolbox

Cites Work

• Unnamed Item
• Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications
• Fast and parallel interval arithmetic
• Fast verification of solutions of matrix equations
• Fast inclusion of interval matrix multiplication
• Accuracy and Stability of Numerical Algorithms
• Fast enclosure of matrix eigenvalues and singular values via rounding mode controlled computation
• Computational error bounds for multiple or nearly multiple eigenvalues

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