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[7].
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