Literature cited
F. Chatelin, Spectral Approximation of Linear Operators, Academic Press, New York (1983).
R. S. Varga, Functional Analysis and Approximation Theory in Numerical Analysis, Society for Industrial and Applied Mathematics, Philadelphia (1971).
G. Strang and G. Fix, An analysis of the Finite Element Method, Pentice-Hall, Englewood Cliffs (1973).
E. G. D'yakonov and M. Yu. Orekhov, “On the minimization of computational work in the determination of the first eigenvalues of differential operators,” Mat. Zametki,27, No. 5, 795–812 (1980).
B. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs (1980).
Y. Saad, “Projection methods for solving large sparse eigenvalue problems,” in: B. Kagström and A. Ruhe (eds.), Matrix Pencils, Lecture Notes in Math., Vol. 973, Springer-Verlag, Berlin-New York (1983), pp. 121–144.
E. G. D'yakonov and A. V. Knyazev, “A group iteration method for the determination of the lowest eigenvalues,” Vestn. Mosk. Gos. Univ., Ser.15, Vychisl. Mat. Kibern., No. 2, 29–34 (1982).
A. V. Knyazev, On the Method of Simultaneous Computation of Several Eigenvectors [in Russian], Preprint IAÉ-3724/16, Moscow (1983).
A. V. Knyazev and V. I. Lebedev, “Estimates of the convergence and analysis of optimality of iteration methods of simultaneous computation of several eigenvectors,” in: Computational Methods of Linear Algebra [in Russian], Otd. Vychisl. Mat. Akad. Nauk SSSR, Moscow (1983), pp. 94–114.
M. A. Krasnosel'skii, G. M. Vainikko, P. P. Zabreiko, and others, Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).
A. V. Knyazev, “On sharp a priori error estimates of the type of inequalities in the Rayleigh-Ritz method for symmetric spectral problems without the assumptions of fixed sign or compactness,” in: Methods of Computational and Applied Mathematics [in Russian], Otd. Vychisl. Mat. Akad. Nauk SSSR, Moscow (1985), pp. 74–88.
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators, Academic Press, New York (1978).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 38, No. 6, pp. 900–907, December, 1985.
The main aim of this note from the beginning has been the generalization of the results of [4], in which D'yakonov took the lead. The author is thankful to him.
Rights and permissions
About this article
Cite this article
Knyazev, A.V. Sharp a priori error estimates of the Rayleigh-Ritz method without assumptions of fixed sign or compactness. Mathematical Notes of the Academy of Sciences of the USSR 38, 998–1002 (1985). https://doi.org/10.1007/BF01157020
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01157020