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

In: Optimization, Simulation, and Control

Author

Listed:
  • Jürgen Garloff

    (University of Applied Sciences / HTWG Konstanz)

  • Evgenija D. Popova

    (Bulgarian Academy of Sciences)

  • Andrew P. Smith

    (University of Applied Sciences / HTWG Konstanz)

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.

Suggested Citation

  • Jürgen Garloff & Evgenija D. Popova & Andrew P. Smith, 2013. "Solving Linear Systems with Polynomial Parameter Dependency with Application to the Verified Solution of Problems in Structural Mechanics," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & E. N. Pistikopoulos (ed.), Optimization, Simulation, and Control, edition 127, pages 301-318, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-5131-0_19
    DOI: 10.1007/978-1-4614-5131-0_19
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