Large-scale matrix diagonalization methods by direct optimization of Taylor expansion of Rayleigh–Ritz quotient up to third order

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.