Adifor Working Note #6: Structured Second-and Higher-order Derivatives through Univariate Taylor Series Structured Second-and Higher-order Derivatives through Univariate Taylor Series Mcs Preprint P296{0392

Second-and higher-order derivatives are required by applications in scientiic computation, especially for optimization algorithms. The two complementary concepts of interpolating partial derivatives from univariate Taylor series and preaccumulating of \local" derivatives form the mathematical foundations for accurate, eecient computation of second-and higher-order partial derivatives for large codes. We compute derivatives in a fashion that parallelizes well, exploits sparsity or other structure frequently found in Hessian matrices, can compute only selected elements of a Hessian matrix, and computes Hessian vector products.