多倍長演算を利用したBessel関数の精度保証付き数値計算(科学技術計算と数値解析(多倍長科学技術計算の基礎と応用), <特集>平成17年研究部会連合発表会)

抄録

Both multiple-precision arithmetic and validated computation have close relationship with the quality of computation. They improve and insure the quality, respectively. We propose a method to compute Bessel functions with guaranteed accuracy, which works on MATLAB. Using multiple-precision arithmetic, the method gives as precise results as one wants together with information of how precise the results are. When it is sufficient to get the results in double-precision, one can use a fast version.