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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Local convergence theory of inexact Newton methods based on structured least change updates
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by José Mario Martínez PDF
Math. Comp. 55 (1990), 143-167 Request permission


In this paper we introduce a local convergence theory for Least Change Secant Update methods. This theory includes most known methods of this class, as well as some new interesting quasi-Newton methods. Further, we prove that this class of LCSU updates may be used to generate iterative linear methods to solve the Newton linear equation in the Inexact-Newton context. Convergence at a q-superlinear rate (or at an "ideal" linear rate, in the sense of Dennis-Walker) of the Inexact Newton methods generated in this way is proved, independently of the number of iterations used in the linear iterative subalgorithm. We apply the new theory to some particular methods.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 55 (1990), 143-167
  • MSC: Primary 65H10; Secondary 90C30
  • DOI:
  • MathSciNet review: 1023050