Zur iterativen Loesung von linearen Gleichungssystemen

TL;DR

This paper introduces a method that ensures convergence of fixed point iterations for solving linear systems, even when the spectral radius condition is not initially satisfied, demonstrated through examples.

Contribution

A novel method is presented that guarantees convergence of fixed point iterations for linear systems without requiring the spectral radius to be less than one.

Findings

Method guarantees convergence regardless of spectral radius

Demonstrated through calculation examples

Extends applicability of fixed point iteration methods

Abstract

It is well known that a fixed point iteration for solving a linear equation system converges if and only if the spectral radius of the iteration matrix is less than one. A method is presented which guarantees the Fixed Point, even if this condition is not ("spectral radius <1") fulfilled and demonstrated through calculation examples.