Rational matrix functions and rank-1 updates (Q2706247)

This paper deals with the efficient computation of \(f(A+ uv^T)\), assuming that \(f(A)\) is available and \(f\) is a prescribed rational function defined on the spectrum of \(A\) and \(A+ uv^T\). A generalized Sherman-Morrison formula is presented. For an application, a Jacobian computation, arising in an inverse problem involving the matrix exponential is considered.