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Large-scale matrix diagonalization methods by direct optimization of Taylor expansion of Rayleigh-Ritz quotient up to third order are presented. Some applications of the quadratic and cubic algorithms, focused in lowest, higher and degenerate roots are discussed and analyzed. The performances of the methods are similar to the Lagrange-Newton-Raphson diagonalization method.
Departament de Quı́mica Orgànica i Centre de Recerca en Quı́mica Teòrica, Universitat de Barcelona, c./ Martı́ i Franquès 1, E–08028 Barcelona, Catalunya, Spain
Departament de Quı́mica Fı́sica i Centre de Recerca en Quı́mica Teòrica, Universitat de Barcelona, c./ Martı́ i Franquès 1, E–08028 Barcelona, Catalunya, Spain
Departament de Quı́mica Fı́sica i Centre de Recerca en Quı́mica Teòrica, Universitat de Barcelona, c./ Martı́ i Franquès 1, E–08028 Barcelona, Catalunya, Spain