In statistical pattern recognition, the parameters of distributions are usually estimated from training sample vectors. However, estimated parameters contain estimation errors, and the errors cause bad influence on recognition performance when the sample size is not sufficient. Some methods can obtain better estimates of the eigenvalues of the true covariance matrix and can avoid bad influences...

The intricate shapes and sounds that arise from vibrating Chladni plates are a well-known phenomenon. They are also quantitatively well understood, as the spatial patterns correspond to the eigenvectors of the underlying plate, and the audio frequencies arise from the plate’s eigenvalues. We explore a generalization of the phenomenon by computing analogous quantities for a computational fluid d...

in this paper we consider the solutions of linear systems of saddle point problems‎. ‎by using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the hermitian and skew hermitian splitting method‎.

Let F(z) be a vector-valued function, F : e _ eN, which is analytic at z= 0 and meromorphic .. in a neighbourhood ofz = 0, and let its Maclaurin series be given. In this work we develop vector­ valued rational approximation procedures for F(z) by applying vector extrapolation methods to the sequence of partial sums of its Maclaurin series. We analyze some of the algebraic and analytic propertie...

let $n$ be any positive integer and let $f_n$ be the friendship (or dutch windmill) graph with $2n+1$ vertices and $3n$ edges. here we study graphs with the same adjacency spectrum as the $f_n$. two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. let $g$ be a graph cospectral with $f_n$. here we prove that if $g$ has no cycle of length $4$ or $...

This dissertation considers algorithms for determining a few of the largest singular values and corresponding vectors of large sparse matrices by solving equivalent eigenvalue problems. The procedure is based on a method by Golub and Kent for estimating eigenvalues of equvalent eigensystems using modified moments. The asynchronicity in the computations of moments and eigenvalues makes this meth...

We develop two approaches for analyzing the approximation error bound for the Nyström method, one based on the concentration inequality of integral operator, and one based on the compressive sensing theory. We show that the approximation error, measured in the spectral norm, can be improved from O(N/ √ m) to O(N/m) in the case of large eigengap, where N is the total number of data points, m is ...

Multiple antennas at the transmitter and the receiver can be used to achieve diversity or multiplexing gain or a combination of the two gains. Most works to date study schemes that achieve either of the two extremes in this diversitymultiplexing trade-off. In this work, we assume communication with a fixed number (M ) of independent data-streams and a linear receiver architecture. Motivated by ...

If G is a simple graph (a non-oriented graph without loops or multiple edges), its (0, 1)-adjacency matrix A is symmetric and roots of the characteristic polynomial PG (λ) = det (λI −A) (the eigenvalues of G, making up its spectrum) are all real numbers, for which we assume their non-increasing order: λ1 ≥ λ2 ≥ · · · ≥ λn. In a connected graph for the largest eigenvalue λ1 (the index of the gra...