Lagrange-Type Iterative Methods for Calculation of Extreme Eigenvalues of Generalized Eigenvalue Problem With Large Symmetric Matrices

The new block and the block diagonal Lagrange iterative methods together with the block generalizations of the Newton-Rayleigh type methods are proposed. It is also shown that the Jacobi-Davidson correction vector is a Newton-Raphson correction vector for the Lagrange functional of the generalized eigenvalue problem. For a simplification of a solution of the Newton-Raphson equation for calculations of correction vectors, a skeleton matrix approximation was introduced and used in the new methods as well in a few known ones. The numerical algorithms of the new methods are described in details and their performances are compared in several numerical test calculations. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 111: 2545-2554, 2011