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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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


Authors: D. Goldfarb and Ph. L. Toint
Journal: Math. Comp. 43 (1984), 69-88
MSC: Primary 65F50; Secondary 65N20
MathSciNet review: 744925
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1984-0744925-5
PII: S 0025-5718(1984)0744925-5
Keywords: Finite differences, sparsity, coverings
Article copyright: © Copyright 1984 American Mathematical Society