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For contractive interval functions $[g]$ we show that $[g] ({[x]}_{ϵ}^{k_{0}}) \subseteq \int ({[x]}_{ϵ}^{k_{0}})$ results from the iterative process ${[x]}^{k + 1} : = [g] ({[x]}_{ϵ}^{k})$ after finitely many iterations if one uses the epsilon-inflated vector ${[x]}_{ϵ}^{k}$ as input for $[g]$ instead of the original output vector ${[x]}^{k}$ . Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way.

Étude de la séparation et de l'élimination sur une famille de graphes quotients déduite d'une méthode de dissections emboîtées

P. Charrier, J. Roman (1988)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Exact Inverses of Certain Band Matrices.

E.L. Allgower (1973)

Numerische Mathematik

Exact Solution of Linear Equations Using P-Adic Expansions

J.D. Dixon (1982)

Numerische Mathematik

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Displaying 1 – 13 of 13

Efficient algorithms for solving nonlinear Volterra integro-differential equations with two point boundary conditions.

Efficient FORTRAN implementation of the gaussian elimination and Householder reduction algorithms on the IBM 3090 vector multiprocessor

Einschließung inverser Elemente durch Fixpunktverfahren.

Elimination on sparse symmetric systems of a special structure

Entrywise perturbation theory and error analysis for Markov chains.

Epsilon-inflation with contractive interval functions

Error Analysis of an Algorithm for Solving an Undetermined Linear System.

Error analysis of some approximating algorithms

Error Analysis of the Björck-Pereyra Algorithms for Solving Vandermonde Systems.

Estudio del error progresivo en la eliminación de Neville

Étude de la séparation et de l'élimination sur une famille de graphes quotients déduite d'une méthode de dissections emboîtées

Exact Inverses of Certain Band Matrices.

Exact Solution of Linear Equations Using P-Adic Expansions

Currently displaying 1 – 13 of 13