An algorithm for the symmetric generalized eigenvalue problem (Q1064011)

A method is presented for the solution of the generalized eigenvalue problem \(Ax=\lambda Bx\), where A and B are real symmetric \(n\times n\) matrices and B is positive semidefinite. The method uses the reduction of matrices to matrices which are of upper triangular and upper Hessenberg form. The convergence of the algorithm is proved and a few numerical examples are given.