Solving Linear Systems with Polynomial Parameter Dependency with Application to the Verified Solution of Problems in Structural Mechanics

Jürgen Garloff (), Evgenija D. Popova () and Andrew P. Smith ()
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Jürgen Garloff: University of Applied Sciences / HTWG Konstanz
Evgenija D. Popova: Bulgarian Academy of Sciences
Andrew P. Smith: University of Applied Sciences / HTWG Konstanz

A chapter in Optimization, Simulation, and Control, 2013, pp 301-318 from Springer

Abstract: Abstract We give a short survey on methods for the enclosure of the solution set of a system of linear equations where the coefficients of the matrix and the right hand side depend on parameters varying within given intervals. Then we present a hybrid method for finding such an enclosure in the case that the dependency is polynomial or rational. A general-purpose parametric fixed-point iteration is combined with efficient tools for range enclosure based on the Bernstein expansion of multivariate polynomials. We discuss applications of the general-purpose parametric method to linear systems obtained by standard finite element analysis of mechanical structures and illustrate the efficiency of the new parametric solver.

Keywords: Interval Arithmetic; Parametric Solver; Parametric Solution; Multivariate Polynomial; Standard Finite Element Method (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-5131-0_19

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DOI: 10.1007/978-1-4614-5131-0_19

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