Solving Very Sparse Rational Systems of Equations

DOI10.1145/1916461.1916463zbMath1365.65121OpenAlexW2053005439WikidataQ113310467 ScholiaQ113310467MaRDI QIDQ2989125

Daniel E. Steffy, William Cook

Publication date: 19 May 2017

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

Full work available at URL: https://doi.org/10.1145/1916461.1916463

zbMATH Keywords

linear programmingsparse matricesLU factorizationrational systemsDixon's algorithmWiedemann's method

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical mathematical programming methods (65K05) Linear programming (90C05) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (6)

Algorithm 1021: SPEX Left LU, Exactly Solving Sparse Linear Systems via a Sparse Left-looking Integer-preserving LU Factorization ⋮ Roundoff-Error-Free Basis Updates of LU Factorizations for the Efficient Validation of Optimality Certificates ⋮ Roundoff-Error-Free Algorithms for Solving Linear Systems via Cholesky and LU Factorizations ⋮ Linear programming using limited-precision oracles ⋮ Iterative Refinement for Linear Programming ⋮ Exact Solution of Sparse Linear Systems via Left-Looking Roundoff-Error-Free LU Factorization in Time Proportional to Arithmetic Work

Uses Software

• FFLAS-FFPACK
• gmp
• LinBox
• NTL
• TSPLIB
• CPLEX
• QSopt

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