Estimating the largest eigenvalue of a positive definite matrix
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- by Dianne P. O’Leary, G. W. Stewart and James S. Vandergraft PDF
- Math. Comp. 33 (1979), 1289-1292 Request permission
Abstract:
The power method for computing the dominant eigenvector of a positive definite matrix will converge slowly when the dominant eigenvalue is poorly separated from the next largest eigenvalue. In this note it is shown that in spite of this slow convergence, the Rayleigh quotient will often give a good approximation to the dominant eigenvalue after a very few iterations-even when the order of the matrix is large.References
- B. N. Parlett and D. S. Scott, The Lanczos algorithm with selective orthogonalization, Math. Comp. 33 (1979), no. 145, 217–238. MR 514820, DOI 10.1090/S0025-5718-1979-0514820-3
- H. Rutishauser, Handbook Series Linear Algebra: Simultaneous iteration method for symmetric matrices, Numer. Math. 16 (1970), no. 3, 205–223. MR 1553979, DOI 10.1007/BF02219773
- G. W. Stewart, Accelerating the orthogonal iteration for the eigenvectors of a Hermitian matrix, Numer. Math. 13 (1969), 362–376. MR 248975, DOI 10.1007/BF02165413
- G. W. Stewart, Introduction to matrix computations, Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1973. MR 0458818
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Math. Comp. 33 (1979), 1289-1292
- MSC: Primary 65F15
- DOI: https://doi.org/10.1090/S0025-5718-1979-0537973-X
- MathSciNet review: 537973