High performance verified computing using C-XSC

DOI10.1007/s40314-013-0028-4zbMath1278.65056OpenAlexW2045825553MaRDI QIDQ382427

Walter Krämer

Publication date: 19 November 2013

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-013-0028-4

zbMATH Keywords

numerical examplesself-validating methodsparallelizationhigh performance computinginterval linear systemverified computing\texttt{C-XSC}packaged methodssparse methodsthread-safety

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Interval and finite arithmetic (65G30) Parallel numerical computation (65Y05) Direct numerical methods for linear systems and matrix inversion (65F05) Algorithms with automatic result verification (65G20) Packaged methods for numerical algorithms (65Y15)

Related Items (1)

Solving interval systems of equations obtained during the numerical solution of boundary value problems

Uses Software

• C-XSC
• C-XSC 2.0
• ScaLAPACK
• UMFPACK
• INTLAB
• CHOLMOD
• FastPILSS
• ParLinSys
• symrcm
• Algorithm 876
• PBLAS
• CSparse

Cites Work

• Inner and outer bounds for the solution set of parametric linear systems
• Dense linear system: A parallel self-verified solver
• Rounding-error and perturbation bounds for the Cholesky and \(LDL^ T\) factorizations
• ScaLAPACK: A portable linear algebra library for distributed memory computers -- design issues and performance
• Verification of positive definiteness
• Condition numbers and equilibration of matrices
• Algorithm 876
• The Arithmetic of the Digital Computer: A New Approach
• Sparse Matrices in MATLAB: Design and Implementation
• Basic Linear Algebra Subprograms for Fortran Usage
• Numerical Software with Result Verification
• Algorithm 832
• Accurate Sum and Dot Product
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• Unnamed Item
• Unnamed Item
• Unnamed Item

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