Topic
Spectrum of a matrix
About: Spectrum of a matrix is a research topic. Over the lifetime, 1064 publications have been published within this topic receiving 19841 citations. The topic is also known as: matrix spectrum.
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TL;DR: In this paper, the convergence rate of the conjugate gradient method is dependent on the eigenvalues of the iteration matrix as well as on the number of eigenvectors needed to represent the right side of the equation.
Abstract: A theory that relates eigenvalues of a continuous operator to those of the moment-method matrix operator is discussed and confirmed by examples. This theory suggests reasons for ill conditioning when certain types of basis and testing functions are used. In addition, the effect of eigenvalue location on the convergence of the conjugate gradient (CG) method is studied. The convergence rate of the CG method is dependent on the eigenvalues of the iteration matrix as well as on the number of eigenvectors of the iteration matrix needed to represent the right side of the equation. These findings explain the previously reported convergence behavior of the CG method when applied to electromagnetic-scattering problems. >
37 citations
TL;DR: In this paper, it was shown that the trivial vacuum, where the phases vanish, is a minimum of the free energy of the Wilson line at nonzero temperature, and the corresponding partition function for the phases of these eigenvalues was constructed.
37 citations
TL;DR: In this article, the spectrum of the electrostatic integral operator of a sphere and a prolate spheroid was shown to lie in the interval [−1, 0] and [− 1, 1] of a smooth surface for which the underlying integral operator has a positive eigenvalue.
36 citations
TL;DR: In this article, the spectral norm of an r-circulant matrix H = Cr(Hk, 0, Hk, 1, hk, 2, n-1) whose entries are the generalized k-Horadam numbers was studied.
Abstract: In this paper, we present new upper and lower bounds for the spectral norm of an r-circulant matrix H = Cr(Hk,0, Hk,1, Hk,2, ... , Hk,n-1) whose entries are the generalized k-Horadam numbers. Furthermore, we obtain new formulas to calculate the eigenvalues and determinant of the matrix H. MSC: 11B39; 15A60; 15A15
36 citations
36 citations