Matrix continued fractions and Expansions of the Error Function

TL;DR

This paper explores the convergence and properties of matrix continued fractions, providing new expansion formulas for the error function when applied to matrices, supported by numerical examples.

Contribution

It introduces novel continued fraction expansions for the matrix error function and analyzes their convergence properties.

Findings

Established convergence criteria for matrix continued fractions

Derived continued fraction expansions for erf(A) with matrices

Provided numerical examples validating theoretical results

Abstract

In this paper we recall some results and some criteria on the convergence of matrix continued fractions. The aim of this paper is to give some properties and results of continued fractions with matrix arguments. Then we give continued fraction expansions of the error function erf(A) where A is a matrix. At the end, some numerical examples illustrating the theoretical results are discussed.