parametric linear system interval parameter polynomial range Bernstein expansion mechanical structure Department of Biomathematics
Issue Date:
Jan-2009
Publisher:
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Citation:
Preprint
Series/Report no.:
2009;1
Abstract:
A wide range of scientific and engineering problems can be described by systems of linear algebraic equations involving uncertain model parameters. We report on new software tools for solving linear systems where the coefficients of the matrix and the right hand side are multivariate polynomials or rational functions of parameters varying within given intervals. A general-purpose parametric fixed-point iteration is combined with efficient tools for range enclosure based on the Bernstein expansion of multivariate polynomials. A C++ software package for constructing the Bernstein enclosure of polynomial ranges, based on the interval library filib++, is integrated into a Mathematica package for solving parametric systems via the MathLink communication protocol. We discuss an advanced application of the general-purpose parametric method to linear systems obtained by standard FEM analysis of mechanical structures and illustrate the efficiency of the new parametric solver. AMS subject classification: 65G20, 15A06, 74S05.
