The Symm-Wilkinson method for improving an approximate eigenvalue and its associated eigenvector (Q792736)

This paper discusses the Symm-Wilkinson method for improving an approximate simple eigenvalue of an \(n\times n\) matrix and a corresponding approximate eigenvector. It is shown that their method is a Newton-like method applied to a system of nonlinear equations so that the process converges linearly under the usual assumptions. It is also shown that the Symm-Wilkinson method needs more multiplications than the standard Newton-like method applied to the same equations by n-1 at each step.