A test for cancellation errors in quasi-Newton methods

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A test for cancellation errors in quasi-Newton methods

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 18 , Issue 2 (June 1992) table of contents

Pages: 134 - 140

Year of Publication: 1992

ISSN:0098-3500

Author

Chaya Gurwitz

Brooklyn College, City Univ. of New York, Brooklyn, NY

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 2, Downloads (12 Months): 24, Citation Count: 1

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abstract references cited by index terms review collaborative colleagues

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ABSTRACT

It has recently been shown that cancellation errors in a quasi-Newton method can increase without bound as the method converges. A simple test is presented to determine when cancellation errors could lead to significant contamination of the approximating matrix.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	AL-BAALI, M., AND FLETCHER, R. Variational methods for nonhnear least squares. J. Oper. Res. Soc. 36 (1985), 405 421.
	2	BYRD, R. H., NOCEDAL, J , AND YUAN, Y. Global convergence of a class of quasi-Newton methods on convex problems. SIAM J. Numer. Anal. 24 (1987), 1171 1190.
	3	FLETCHER, R. Function minimization without evaluating derivatives--A review. Coraput. J 8 (1965), 33-41.
	4	R. Fletcher, Practical methods of optimization; (2nd ed.), Wiley-Interscience, New York, NY, 1987
	5	R Fletcher, Cancellation errors in quasi Newton methods, SIAM Journal on Scientific and Statistical Computing, v.7 n.4, p.1387-1399, Oct. 1986 [doi>10.1137/0907092]
	6	FLETCHER, R., AND POWELL, M J. D A rapidly convergent descent method for minimization. Comput. J. 6 (1963), 163-168.
	7	M J D Powell, How bad are the BFGS and DFP methods when the objective function is quadratic?, Mathematical Programming: Series A and B, v.34 n.1, p.34-47, Jan. 1986 [doi>10.1007/BF01582161]
	8	William H. Press , Brian P. Flannery , Saul A. Teukolsky , William T. Vetterling, Numerical recipes: the art of scientific computing, Cambridge University Press, New York, NY, 1986
	9	Robert B. Schnabel , John E. Koonatz , Barry E. Weiss, A modular system of algorithms for unconstrained minimization, ACM Transactions on Mathematical Software (TOMS), v.11 n.4, p.419-440, Dec. 1985 [doi>10.1145/6187.6192]
	10	D. F. Shanno , K. H. Phua, Remark on “Algorithm 500: Minimization of Unconstrained Multivariate Functions [E4]”, ACM Transactions on Mathematical Software (TOMS), v.6 n.4, p.618-622, Dec. 1980 [doi>10.1145/355921.355933]

CITED BY

E. G. Birgin , J. M. Martínez, Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization, Computational Optimization and Applications, v.39 n.1, p.1-16, January 2008

INDEX TERMS

Primary Classification:
G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS

Additional Classification:
G. Mathematics of Computing
G.4 MATHEMATICAL SOFTWARE
Subjects: Reliability and robustness

General Terms:
Algorithms

Keywords:
cancellation error, quasi-Newton update, unconstrained optimization

REVIEW

"Florin Popentiu : Reviewer"

Gurwitz describes a heuristic test for estimating the effect of the cancellation error on the approximating matrix in quasi-Newton methods. After a review of the theoretical results (which are largely due to R. Fletcher more...

Collaborative Colleagues:

Chaya Gurwitz: colleagues

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