A minimization method for the solution of large symmetric eigenproblems

This paper concerns with the solution of a special eigenvalue problem for a large sparse symmetric matrix by a fast convergent minimization method. A theoretical analysis of the method is developed; it is proved that is conve rgent with a convergence rate of fourth order. This minimization method req uires to solve a sequence of equality-constrained least squares problems th at become increasingly ill-conditioned, as the solution of eigenvalue probl em is approached, A particular attention has been addressed to this questio n of ill-conditioning for the practical application of the method. Computat ional experiments carried out on Gray C90 show the behaviour of this minimi zation method as accelerating technique of the inverse iteration method. Al so a comparison with the scaled Newton method has been done.