Solving nonlinear systems with least significant bit accuracy

DOI10.1007/BF02241697zbMath0485.65036OpenAlexW3183121460MaRDI QIDQ1164379

Siegfried Michael Rump

Publication date: 1982

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02241697

zbMATH Keywords

existenceuniquenesscondition numberautomatic verificationresiduerounding errorinclusion of the solution

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10)

Related Items (14)

Componentwise inclusion and exclusion sets for solutions of quadratic equations in finite dimensional spaces ⋮ Safe starting regions by fixed points and tightening ⋮ A circuit for exact summation of floating-point numbers ⋮ Experiences with a method for enclosing solutions of systems of equations ⋮ Verified solution of large systems and global optimization problems ⋮ Numerical method for verifying the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation ⋮ Least significant bit evaluation of arithmetic expressions in single- precision ⋮ Solving nonlinear parabolic problems with result verification. I: One- space dimensional case ⋮ An enclosure method of eigenvalues for the elliptic operator linearized at an exact solution of nonlinear problems ⋮ Rigorous Sensitivity Analysis for Systems of Linear and Nonlinear Equations ⋮ A framework for existence tests based on the topological degree and homotopy ⋮ Some techniques for solving linear equation systems with guarantee ⋮ Accurate arithmetic results for decimal data on non-decimal computers ⋮ Verified numerical computations for multiple and nearly multiple eigenvalues of elliptic operators

Cites Work

• E-methods for fixed point equations f(x)=x
• Least significant bit evaluation of arithmetic expressions in single- precision
• Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken
• Solving nonlinear simultaneous equations with a generalization of Brent's method
• Fast local convergence with single and multistep methods for nonlinear equations
• A Test for Existence of Solutions to Nonlinear Systems
• Numerical Solution of Nonlinear Equations
• Polynomial Minimum Root Separation
• Floating-Point Computation of Functions with Maximum Accuracy
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