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The solution of systems of equations using the $ \varepsilon $-algorithm, and an application to boundary-value problems

Authors: Claude Brezinski and Alain C. Rieu
Journal: Math. Comp. 28 (1974), 731-741
MSC: Primary 65H10
MathSciNet review: 0381288
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Abstract: In this paper, the authors describe the properties of an algorithm to solve systems of nonlinear equations. The algorithm does not use any derivatives. The convergence of this algorithm is quadratic under quite mild conditions. This method can also be used to solve systems of linear equations with infinitely many solutions. The second part of the paper is devoted to the application of this algorithm to the solution of multipoint boundary-value problems for differential equations. A theorem of convergence is proved and various numerical examples are given.

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Keywords: Solution of systems of equations, algorithm with quadratic convergence, boundary-value problem, differential equations
Article copyright: © Copyright 1974 American Mathematical Society

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