Abstract
The paper presents upper bounds for the largest eigenvalue of a block Jacobi scaled symmetric positive-definite matrix which depend only on such parameters as the block semibandwidth of a matrix and its block size. From these bounds we also derive upper bounds for the smallest eigenvalue of a symmetric matrix with identity diagonal blocks. Bibliography: 4 titles.
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Literature Cited
O. Axelsson and L. Kolotilina, “Diagonally compensated reduction and related preconditioning methods,” Catholic Univ. Nijmegen, Dept. of Mathematics, Rept. 9117, Aug. 1991 (to appear inNumer. Linear Alg. Appl.).
L. A. Hageman and D. M. Young,Applied Iterative Methods, New York (1981).
J. M. Ortega,Numerical Analysis, A Second Course, New York (1972).
V. V. Voevodin and Yu. A. Kuznetsov,Matrices and Computation [in Russian], Moscow (1984).
Additional information
Translated by L. Yu. Kolotilina.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 202, 1992, pp. 18–25.
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Kolotilina, L.Y. Bounds for eigenvalues of symmetric block Jacobi scaled matrices. J Math Sci 79, 1043–1047 (1996). https://doi.org/10.1007/BF02366126
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DOI: https://doi.org/10.1007/BF02366126