Parametric Fixed-Point Iteration Implemented in C-XSC Evgenija Popova

Consider linear systems whose matrix and right-hand side vector depend affinelinearly on parameters varying within prescribed intervals. We present a C-XSC [9] implementation of a parametric fixed-point iteration method for the verified enclosure of the parametric solution set. Input data for the system have an entirely numerical representation by dense twodimensional matrices. Some specific features of the corresponding algorithm concerning sharp enclosure of the contracting matrix, epsilon inflation, and inner approximation of the solution enclosure are discussed. Numerical examples illustrate the application of the presented software and the discussed specific features of the algorithm. Our software seems to be the first open source software delivering verified results in the field of parametric linear systems (inner and outer estimations for the hull of the solution set). The source code is available at http://www.math.uni-wuppertal.de/wrswt/xsc/cxsc − oftware.html . The software will be developed further.

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