Numerical methods for finding multiple eigenvalues of matrices depending on parameters (Q1358151)

An incomplete QR decomposition is used to determine the multiple eigenvalues of square matrices \(A(\alpha, \lambda)\) which depend upon two parameters \(\alpha\) and \(\lambda\) where \(\lambda\) is the eigenvalue parameter. Two algorithms are displayed for multiple eigenvalues with geometrical multiplicity larger than unity, and another one is provided in the case of unit geometrical multiplicity. It is shown that the iterates generated by the algorithms do not depend upon the QR decomposition.