On the methods of simultaneous calculation of several eigenvectors

Numerical methods of simultaneous determination of several minor eigenvalues (e. v.) and eigensubspaces (e. s. s.), corresponding to them, of generalized problem for eigenvalues with symmetric and positively defined matrices are considered. From simple ratios for subspace solutions in various metrics, a precision of approximations to e.v. according to the Ritz method is eszimated, which leads to evaluation of precision of approximations to e. s. s. in terms of solutions. Evaluations of the convergence rate (c. r.) of inequality types, for methods of simultaneous iterations are obtained. The concept of the optimality is determined on their basis. It is shown that evaluations of c. r. of the optimum method of simultaneous iterations can not be improved. Evaluations of c. r. of the block Lanczos method, clarifying the known ones, are presented