多倍長浮動小数点演算と補外を用いた数値微分法に基づくJacobi行列計算 Jacobian Matrix Computation based on Numerical Differentiation Using Multiple Precision Floating-point Arithmetic and Extrapolation
Nowadays, the Jacobian matrix computation is usually based on automatic differentiation(AD). Unless AD can be applied, numerical differentiation is selected. In this case, it generally yields a low precision. However, we can obtain an arbitrary precision Jacobian matrix by using extrapolation and multiple-precision floating-point arithmetic. In this paper, we propose an arbitrary precision numerical computation method of Jacobian matrix based on numerical differentiation using extrapolation, and demonstrate its efficiency through numerical experiments using MPFR.
日本応用数理学会論文誌 17(2), 173-182, 2007