Solvers for the verified solution of parametric linear systems

DOI10.1007/s00607-011-0170-zzbMath1238.65021OpenAlexW2079386241MaRDI QIDQ411424

Walter Krämer, Evgenija D. Popova, Michael F. Zimmer

Publication date: 4 April 2012

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-011-0170-z

zbMATH Keywords

algorithmnumerical examplessparse matricesdense matricesC-XSCparameter dependent systemperformance measurementsself-verifying solversparse data structure

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Parallel numerical computation (65Y05) Complexity and performance of numerical algorithms (65Y20) Direct numerical methods for linear systems and matrix inversion (65F05) Algorithms with automatic result verification (65G20) Error analysis and interval analysis (65G99)

Related Items (3)

Solving over-constrained systems of non-linear interval equations -- and its robotic application ⋮ An extension of the \(\alpha\mathrm{BB}\)-type underestimation to linear parametric Hessian matrices ⋮ On preconditioning and solving an extended class of interval parametric linear systems

Uses Software

• C-XSC
• C-XSC 2.0
• LAPACK
• CLAPACK
• BLAS
• INTLAB
• FastPILSS
• ParLinSys

Cites Work

• Inner and outer bounds for the solution set of parametric linear systems
• Parametric interval linear solver
• Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken
• Verification methods: Rigorous results using floating-point arithmetic
• Generalization of a Parametric Fixed-Point Iteration
• The Arithmetic of the Digital Computer: A New Approach
• LAPACK Users' Guide
• Numerical Software with Result Verification
• Worst-case tolerance analysis of linear DC and AC electric circuits
• An updated set of basic linear algebra subprograms (BLAS)
• Accurate Sum and Dot Product
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