Petrov Method Research Articles

Galerkin–Petrov Methods for Bergman Space Toeplitz Operators

The convergence of several Galerkin-Petrov methods is established, including polynomial collocation and analytic element collocation methods, for Toeplitz operators on the Bergman space of the unit disk. In particular, it is shown that such methods converge if the basis and test functions (or the collocation points) own certain circular symmetry, whereas unfortunate choice of the basis and test parameters produces nonconvergent Galerkin–Petrov methods.

A characterization of pairs of subspaces for quantum chemical applications of the Galerkin–Petrov method

AbstractA method is proposed for characterizing pairs of finite dimensional subspaces of the Hilbert space. The method might be helpful for the proper selection of coordinate and projective spaces leading to reliable realizations of the Galerkin–Petrov method for use in quantum chemistry. In order to illustrate the method some numerical results are presented.

Applicability of the Galerkin—Petrov method in quantum chemistry. The quartic oscillator problem

The use of a scheme based on the Galerkin—Petrov method for quantum chemical calculations is suggested.The results of its application to the calculation of the ground and excited states of the quartic oscillator are presented.

On the speed of convergence of approximate methods in the eigenvalue problem

THE rate of convergence of projection methods (the Galerkin — Petrov method) in the eigenvalue problem is estimated in [1]. Similar estimates are obtained below for a wider class of methods, including, in particular, methods considered in the general theory of approximate computations [2].