Adaptive Routines for Forming Jacobians Numerically

摘要

Three routines for computing the matrix of partial derivatives (Jacobian) for a system of nonlinear equations are presented. The routines are intended for use in codes for solving nonlinear problems. By taking advantage of the way the Jacobian is evaluated in nonlinear codes, each routine is able to produce more accurate and reliable numerical derivatives with little additional overhead. Two of the routines take advantage of the structure of a Jacobian and can significantly reduce the cost of computing it. 14 refs., 3 tabs. (ERA citation 11:055674)