Existence and uniqueness of solutions of linear sparse matrix equations via a fixed point theorem

TL;DR

This paper extends a fixed point theorem to establish the existence and uniqueness of solutions for linear sparse matrix equations, providing a theoretical foundation for solving such problems.

Contribution

It generalizes a fixed point theorem and applies it to prove solution existence and uniqueness for linear sparse matrix equations.

Findings

Proved existence of solutions for linear sparse matrix equations.

Established uniqueness of solutions under certain conditions.

Extended fixed point theorem applicability to sparse matrices.

Abstract

In this paper, we prove several generalizations and applications of a fixed point theorem. This theorem is used to prove the existence and uniqueness of solutions of the linear sparse matrix problem considered.