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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01 Jan 2005
TL;DR: In this article, the eigenvalues of two versions of W related to some easily specified graphs, and some approximations to the determinant of I - bW are considered. But the evaluation of determinant can still be slow.
Abstract: Exact Gaussian maximum likelihood estimation for a spatial process requires evaluation of the determinant and inverse of the covariance matrix. In geographic modelling, it is common to specify the inverse matrix in terms of I - bW, for some known matrix W, but the evaluation of the determinant can still be slow, even when expressed as a function of the eigenvalues of W. This paper considers the eigenvalues of two versions of W related to some easily specified graphs, and some approximations to the determinant of I - bW.
1 citations
TL;DR: The method is the counterpart of the Rayleigh-Ritz method in the sense that the results obtained from both methods will improve, i.e. the eigenvalues can be bracketed into a small region, and the lower bounds to all eigen values can be obtained from the solution of one transcendental equation.
1 citations
Posted Content•
TL;DR: In this paper, the existence of eigenvalues and eigenfunctions of 1-homogeneous fully nonlinear operators has been studied in the framework of viscosity solutions.
Abstract: In this paper we present an elementary theory about the existence of eigenvalues for fully nonlinear radially symmetric 1-homogeneous operators. A general theory for first eigenvalues and eigenfunctions of 1-homogeneous fully nonlinear operators exists in the framework of viscosity solutions. Here we want to show that for the radially symmetric operators (and one dimensional) a much simpler theory can be established, and that the complete set of eigenvalues and eigenfuctions characterized by the number of zeroes can be obtained.
1 citations
1 citations
1 citations