A note on direct methods for approximations of sparse Hessian matrices
Tůma, Miroslav
Applications of Mathematics, Tome 33 (1988), p. 171-176 / Harvested from Czech Digital Mathematics Library
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Necessity of computing large sparse Hessian matrices gave birth to many methods for their effective approximation by differences of gradients. We adopt the so-called direct methods for this problem that we faced when developing programs for nonlinear optimization. A new approach used in the frame of symmetric sequential coloring is described. Numerical results illustrate the differences between this method and the popular Powell-Toint method.

Publié le : 1988-01-01
Classification:  65D15,  65D25,  65F20,  65H10,  65K05,  90C30 
@article{104300,
     author = {Miroslav T\r uma},
     title = {A note on direct methods for approximations of sparse Hessian matrices},
     journal = {Applications of Mathematics},
     volume = {33},
     year = {1988},
     pages = {171-176},
     zbl = {0658.65058},
     mrnumber = {0944781},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104300}
}

Tůma, Miroslav. A note on direct methods for approximations of sparse Hessian matrices. Applications of Mathematics, Tome 33 (1988) pp. 171-176. http://gdmltest.u-ga.fr/item/104300/

T. F. Coleman J. J. Moré Estimation of Sparse Hessian Matrices and Graph Coloring Problems, Math. Prog. 28 (1984), 243-270. (1984) | Article | MR 0736293

G. C. Everstine A Comparison of Three Resequencing Algorithms for the Reduction of Matrix Profile and Wavefront, International Journal on Numerical Methods in Engineering 14 (1979), 837-853. (1979) | Article | Zbl 0401.73082

A. George J. W. H. Liu Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, Inc. Englewood Cliffs. N. J. 07632, 1981. (1981) | MR 0646786

P. Hanzálek J. Hřebíček J. Kučera A Conversational Program System for Mathematical Optimization, Computer Physics Communications 41 (1986), 403 - 408. (1986) | Article

D. M. Matula L. L. Beck Smallest-last Ordering and Clustering and Graph Coloring Algorithms, JACM 30 (1983), 417-427. (1983) | Article | MR 0709826

S. T. Mccormick Optimal Approximation of Sparse Hessians and its Equivalence to a Graph Coloring Problem, Math. Prog. 26 (1983), 153-171. (1983) | Article | MR 0700644 | Zbl 0507.65027

M. J. D. Powell; Ph. L. Toint On the Estimation of Sparse Hessian Matrices, SIAM on Num. Anal. 16 (1979), 1060-1074. (1979) | Article | MR 0551326 | Zbl 0426.65025

M. N. Thapa Optimization of Unconstrained Functions with Sparse Hessian Matrices: Newton-type Methods, Math. Prog. 19 (1984), 156-186. (1984) | MR 0745406 | Zbl 0538.49023

O. C. Zienkiewicz The Finite Element Method, McGraw Hill, London, 1977. (1977) | Zbl 0435.73072