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The purpose of this talk is primarily to introduce a new methodology to synthesize numerically accurate programs for the Gaussian elimination method in order to solve linear systems coming from mechanical problems. The synthesis is based on program transformation techniques and it is guided in its estimation of accuracy by interval arithmetic that computes the propagation of roundoff errors. Besides a discussion on numerical accuracy issues related to floating-points arithmetics and roundoff errors, we present our approach used to compute the error bound during the resolution process. Finally, some experimental results will be presented to prove the efficiency of our synthesizer tool and show that the specialized produced code to solve the family of systems given in input is far more accurate and faster than the standard implementation of the Gauss method.

Toward the Synthesis of Gauss Pivoting Code for Linear Systems Resolution : Application Mechanical Problems