Computing primary solutions of equations involving primary matrix functions (Q1625478)

The authors examine the matrix equation \(f(X) = A\), where \(f\) is a complex analytic function and \(A\) is a square matrix. They classify some of the solutions to this equation, particularly, in terms of their eigenvalues, those solutions \(X\) which can be expressed as a polynomial in \(A\). The authors also present an algorithm for numerically computing the solutions to \(f(X)=A\), first for the cases in which \(f\) is a rational function and \(A\) is a block upper diagonal, and then more generally.