Estimating the largest eigenvalue of a positive definite matrix
نویسندگان
چکیده
منابع مشابه
Estimating the Largest Eigenvalue of a Positive Definite Matrix
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 m...
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We derive an algorithm for estimating the largest p ≥ 1 values aij or |aij | for an m×n matrix A, along with their locations in the matrix. The matrix is accessed using only matrix– vector or matrix–matrix products. For p = 1 the algorithm estimates the norm ‖A‖M := maxi,j |aij | or maxi,j aij . The algorithm is based on a power method for mixed subordinate matrix norms and iterates on n × t ma...
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Recent progress in signal processing and estimation has generated considerable interest in the problem of computing the smallest eigenvalue of a symmetric positive definite Toeplitz matrix. Several algorithms have been proposed in the literature. Many of them compute the smallest eigenvalue in an iterative fashion, relying on the Levinson–Durbin solution of sequences of Yule–Walker systems. Exp...
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In this paper we suggest a hybrid method for computing the smallest eigenvalue of a symmetric and positive definite Toeplitz matrix which takes advantage of two types of methods, Newton’s method for the characteristic polynomial and projection methods based on rational interpolation of the secular equation.
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Recent progress in signal processing and estimation has generated considerable interest in the problem of computing the smallest eigenvalue of symmetric positive definite Toeplitz matrices. Several algorithms have been proposed in the literature. Many of them compute the smallest eigenvalue in an iterative fashion, relying on the Levinson–Durbin solution of sequences of Yule–Walker systems. Exp...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1979
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1979-0537973-x