Optimal estimation of Jacobian and Hessian matrices that arise in finite difference calculations-Reference-Cited by-同舟云学术

Optimal estimation of Jacobian and Hessian matrices that arise in finite difference calculations

Published:1984 Issue:167 Volume:43 Page:69-88
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Goldfarb D.,Toint Ph. L.

Abstract

In this paper, the problem of estimating Jacobian and Hessian matrices arising in the finite difference approximation of partial differential equations is considered. Using the notion of computational molecule or stencil, schemes are developed that require the minimum number of differences to estimate these matrices. A procedure applicable to more complicated structures is also given.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1984-43-167/S0025-5718-1984-0744925-5/S0025-5718-1984-0744925-5.pdf

Reference15 articles.

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4. T. F. Coleman & J. J. Moré, Estimation of Sparse Hessian Matrices and Graph Colouring Problems, Technical Report ANL-81-535, Argonne National Laboratory, Argonne, Illinois, 1982.

5. A. Curtis, M. J. D. Powell & J. Reíd, "On the estimation of sparse Jacobian matrices," J. Inst. Math. Appl., v. 13, 1974, pp. 117-119.

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