Computing Derivatives of Eigensystems by the Vector {varepsilon}-Algorithm

Rudisill & Chu proposed a (slowly converging) iterativemethod for computing partial derivatives of eigenvalues andeigenvectors of parameter-dependent matrices. It is shown that,with exact computation, application of the vector -algorithmto this method produces the exact solution in a small numberof steps. Numerical results demonstrate the viability of thismethod. A refinement process is suggested which makes the methodespecially effective for subdominant eigenvalues.