Abstract
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.
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Literature cited
D. K. Faddeev and V. N. Faddeva, Computational Methods of Linear Algebra, Freeman, San Francisco (1943).
G. V. Savinov, “The investigation of the convergence of the generalized method of conjugate gradients for some algebra problems,” Candidate's Dissertation, Leningrad (1980).
D. M. Young, Iterative Solution of Large Linear Systems, Academic Press, New York (1971).
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instita im. V. A. Steklova AN SSSR, Vol. 111, pp. 145–150, 1981.
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Savinov, G.V. Convergence of a generalized method of conjugate gradients for the determination of the extremal eigenvalues of a matrix. J Math Sci 24, 95–98 (1984). https://doi.org/10.1007/BF01230270
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DOI: https://doi.org/10.1007/BF01230270