Structure and efficient Hessian calculation
Cornell Theory Center, Cornell University, 1996 - Mathematics - 11 pages
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A.W. Bojanczyk ADOL-C Advanced Computing Research application of sparse apply automatic differentiation arrival of robust Arun Verma Aty-J)T automatic differentiation directly automatic differentiation tools bi-coloring technique calculate the Newton code to evaluate component function composite function example Computer Science Computing Research Institute computing the Hessian Cornell University define dense Dynamical Systems Efficient Hessian Calculation eliminate the 2,2)-block evaluate the gradient extended function Fb extended Hessian matrix FB to obtain given in Figure gradient function Hb directly intermediate vector Jacobian matrix Jacobian of F Kim-Chuan Toh linear algebra Lloyd N MATLAB matrix H matrix Jb Newton step Nikos Chrisochoides objective function partial separable structure perhaps the Newton program to evaluate respect scalar-valued function second derivatives Section 2.2 Solve for y2 sparse AD techniques sparsity structural ideas discussed Structure and Efficient Structured Computation structured program Techniques for Toeplitz Theory Center Thomas F Toeplitz and Toeplitz-Plus-Hankel Trefethen V\yg vector function wTFB(x,y