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

Brezinski, Claude; Rieu, Alain C.

doi:10.1090/S0025-5718-1974-0381288-5

The solution of systems of equations using the $\varepsilon$-algorithm, and an application to boundary-value problems
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by Claude Brezinski and Alain C. Rieu PDF

Math. Comp. 28 (1974), 731-741 Request permission

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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