Maximizing the smallest eigenvalue of a symmetric matrix: A submodular optimization approach
نویسندگان
چکیده
منابع مشابه
Maximizing the Smallest Eigenvalue of a Symmetric Matrix: A Submodular Optimization Approach
This paper studies the problem of selecting a submatrix of a positive definite matrix in order to achieve a desired bound on the smallest eigenvalue of the submatrix. Maximizing this smallest eigenvalue has applications to selecting input nodes in order to guarantee consensus of networks with negative edges as well as maximizing the convergence rate of distributed systems. We develop a submodul...
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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 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: Automatica
سال: 2018
ISSN: 0005-1098
DOI: 10.1016/j.automatica.2018.06.016