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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Quasi-nonexpansivity and two classical methods for solving nonlinear equations
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by St. Măruşter PDF
Proc. Amer. Math. Soc. 62 (1977), 119-123 Request permission

Abstract:

Let F: ${{\mathbf {R}}_n} \to {{\mathbf {R}}_n}$ be a vector-valued function and let $J(x)$ denote the corresponding Jacobi matrix. The main result states that the functions $x - {J^{ - 1}}(x) \cdot F(x)$ and $x - \lambda {J^T}(x)\cdot F(x)$, where $\lambda$ is a certain positive number, are quasi-nonexpansive. This property is used for establishing the convergence of the Newton and the gradient methods in a finite-dimensional space.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 62 (1977), 119-123
  • MSC: Primary 65H05
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0455354-4
  • MathSciNet review: 0455354