Eigenvalues of Ax = λBx for real symmetric matrices A and B computed by reduction to a pseudosymmetric form and the HR process

The paper presents a method for solving the eigenvalue problem Ax = λBx, where A and B are real symmetric but not necessarily positive definite matrices, and B is nonsingular. The method reduces the general case into a form Cz = λz where C is a pseudosymmetric matrix. A further reduction of C produces a tridiagonal pseudosymmetric form to which the iterative HR process is applied. The tridiagonal pseudosymmetric form is invariant under the HR transformations. The amount of computation is significantly less than in treating the problem by a general method.