Year: 2024
Type: article
Abstract: The implementation of Newton’s method for solving nonlinear equations in abstract domains requires the inversion of a linear operator at each step. Such an inversion may be computationally very expensive or impossible to find. That is why alternative iterative methods are developed in this article that require no inversion or only one inversion of a linear operator at each step. The inverse of the operator is replaced by a frozen sum of linear operators depending on the Fréchet derivative of an operator. The numerical examples illustrate that for all practical purposes, the new methods are as effective as Newton’s but much cheaper to implement. The same methodology can be used to create similar alternatives to other methods using inversions of linear operators such as divided differences or other linear operators.
Source: Mathematics
DOI: 10.3390/math12071069
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4393558970