On the computational and numerical approaches for the powers of the doubly Lefkovitch matrix by linear difference equations

Abstract

We explore here a study to derive purely explicit formulas for entries of the \(n-th\) powers of doubly Lefkovitch matrices. Our tool is based on some linear properties of difference equations, including recursive, analytical and derivative aspects of solutions to these equations. Three algorithms for computing the entries of the powers of doubly Lefkovitch matrix are built. Moreover, illustrative applications and examples are furnished.