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Mathematics of Computation

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On the relation between two local convergence theories of least-change secant update methods

Author: José Mario Martínez
Journal: Math. Comp. 59 (1992), 457-481
MSC: Primary 65K10; Secondary 65H10
MathSciNet review: 1136223
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Abstract: In this paper, we show that the main results of the local convergence theory for least-change secant update methods of Dennis and Walker (SIAM J. Numer. Anal. 18 (1981), 949-987) can be proved using the theory introduced recently by Martinez (Math. Comp. 55 (1990), 143-167). In addition, we exhibit two generalizations of well-known methods whose local convergence can be easily proved using Martínez's theory.

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Keywords: Nonlinear systems, quasi-Newton methods, secant methods, least-change secant update methods
Article copyright: © Copyright 1992 American Mathematical Society