A program converter for algorithm stabilization technique

Abstract

In symbolic-numeric computations, an algorithm stabilization technique proposed by Shirayanagi and Sweedler is used effectively. The technique is accomplished by the interval arithmetic and zero-rewriting for given algorithm. They have already proven the algorithm stabilization theorem in for the case that input algorithm is algebraic and input value is exact. However, the application range of the technique is unknown still and various applications are expected. Therefore, we developed a system which performs to transform an input program to stabilized one automatically. Input program to the system is restricted to a program written in Asir language. In this paper, we consider the case that an input program is C language and implement a prototypical system which perfoms to transform a program in C language to stabilized one in Asir language automatically. First, an input program written in C language is converted to a program in Asir language with the interval arithmetic. Then the program is translated into the stabilized program. The stabilized program is executed in computer algebra system Risa/Asir. Examples are also shown.