AUTOMATIC DIFFERENTIATION OF THE VECTOR THAT SOLVES A PARAMETRIC LINEAR-SYSTEM

[摘要] We consider a parametric linear system a(s).x(s) = b(s) where a(s) is a regular matrix, b(s) is a vector, and s is a p-dimensional parameter. This equation represents an implicit definition of a function x. It is shown that automatic differentiation techniques can be used to compute derivatives of x for given parameter-value s. Especially we aim at the Jacobian matrix and the Hessian tensor of x. These quantities are of particular interest in sensitivity analysis and structural optimization.

[发布日期] 1991-06-26

[效力级别]  Proceedings Paper

[关键词] AUTOMATIC DIFFERENTIATION;PARAMETRIC LINEAR EQUATIONS