Convergence of a generalized method of conjugate gradients for the determination of the extremal eigenvalues of a matrix

For the determination of the minimal eigenvalue of a symmetric positive-definite matrix one obtains an estimate of the asymptotic rate of convergence of a generalized method of conjugate gradients, based on the method of the symmetric upper relaxation. One establishes the asymptotic value of the relaxation parameter.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instita im. V. A. Steklova AN SSSR, Vol. 111, pp. 145–150, 1981.