Verified solution of large systems and global optimization problems

DOI10.1016/0377-0427(94)00092-FzbMath0866.65035MaRDI QIDQ1900761

Siegfried Michael Rump

Publication date: 13 July 1997

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

zbMATH Keywords

global optimizationnumerical resultserror boundsinterval arithmeticresult verificationtest examplesbanded sparse systems

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Numerical computation of solutions to systems of equations (65H10) Interval and finite arithmetic (65G30)

Related Items (1)

Interval algorithm for absolute value equations

Uses Software

• PROFIL/BIAS
• LINPACK
• BRENT
• PASCAL-XSC

Cites Work

• Constrained global optimization: algorithms and applications
• Automatic differentiation: techniques and applications
• Solving nonlinear systems with least significant bit accuracy
• A numerical verification method for the existence of weak solutions for nonlinear boundary value problems
• Numerical existence proofs and explicit bounds for solutions of nonlinear elliptic boundary value problems
• On computing the range of a rational function of n variables over a bounded region
• PROFIL/BIAS - A fast interval library
• Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken
• A stochastic method for global optimization
• Condition Estimates
• Rigorous Sensitivity Analysis for Systems of Linear and Nonlinear Equations
• Interval Methods for Systems of Equations
• Fast local convergence with single and multistep methods for nonlinear equations
• On Solving Systems of Equations Using Interval Arithmetic
• Modern Error Analysis
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