Symmetric schemes for computing the minimum eigenvalue of a symmetric Toeplitz matrix
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چکیده
منابع مشابه
Symmetric Schemes for Computing the Minimum Eigenvalue of a Symmetric Toeplitz Matrix
In 8] and 9] W. Mackens and the present author presented two generalizations of a method of Cybenko and Van Loan 4] for computing the smallest eigenvalue of a symmetric, positive deenite Toeplitz matrix. Taking advantage of the symmetry or skew symmetry of the corresponding eigenvector both methods are improved considerably.
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In this note we discuss a method of order 1 + √ 3 for computing the smallest eigenvalue λ1 of a symmetric and positive definite Toeplitz matrix. It generalizes and improves a method introduced in [7] which is based on rational Hermitean interpolation of the secular equation. Taking advantage of a further rational approximation of the secular equation which is essentially for free and which yiel...
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A projection method for computing the minimal eigenvalue of a symmetric and positive deenite Toeplitz matrix is presented. It generalizes and accelerates the algorithm considered in 12]. Global and cubic convergence is proved. Randomly generated test problems up to dimension 1024 demonstrate the methods good global behaviour.
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In this paper, we apply the preconditioned Lanczos (PL) method to compute the minimum eigenvalue of a symmetric positive definite Toeplitz matrix. The sine transform-based preconditioner is used to speed up the convergence rate of the PL method. The resulting method involves only Toeplitz and sine transform matrix-vector multiplications and hence can be computed efficiently by fast transform al...
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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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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1999
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(98)10147-7