PDE Seminar

DATE2016-11-23 15:10-16:00

PLACE數學館 3F會議室


TITLEDesign and Implementation of Multiple-Precision Arithmetic on MATLAB and Its Applications to Numerically Unstable Problems

ABSTRACT In this presentation, a new multiple-precision arithmetic environment on MATLAB is introduced. MATLAB is widely used in numerical computations, and double precision arithmetic which has approximately 16 decimal digits accuracy is used. In numerical treatments of unstable problems, rounding errors give serious influences to results. The proposed environment provides approximation and arithmetic of real numbers with arbitrary accuracy, and is effective to overcome numerical instability. Four basic rules are implemented in assembly language for the sake of fast computations, and it runs on MATLAB (2016b) on MacOSX and Windows at present. Comparisons between VPA (variable precision arithmetic) in MATLAB Symbolic Math Toolbox will be presented, and some demonstrations will be also exhibited.