Computer Algebra for Guaranteed Accuracy. How Does It Help?

Abstract

Today simulation technologies (based on numerical computation) aredefinitely vital in many fields of science and engineering.The accuracy of numerical simulations grows in importance as simulationtechnologies develop and prevail, and many researches have been carriedout for establishing numerically stable algorithms.In recent years, combining computer algebra and other guaranteedaccuracy approaches draws much attention as one of promising directionsfor developing guaranteed accuracy algorithms for a wider class ofproblems. This paper illustrates several typical usages of symbolic andalgebraic methods for guaranteed accuracy computation, highlightingsome of the recent applications in control problems.