This paper presents an explicit expression for the marginal probability density distribution of the unordered eigenvalues of a noncentral Wishart matrix HH† where H can represent a multiple-input multiple-output channel obeying the Ricean law. By integrating over this marginal density distribution, the corresponding ergodic mutual information is characterized also in explicit form.

A multi-rate discrete-time model, whose response agrees exactly with that of a continuous-time original at all sampling instants for any sampling periods, is developed for a linear system, which is assumed to have multiple real eigenvalues. The sampling rates can be chosen arbitrarily and individually, so that their ratios can even be irrational. The state space model is obtained as a combinati...

The main advantage of inverse iteration over the QR algorithm and Divide & Conquer for the symmetric tridiagonal eigenproblem is that subsets of eigenpairs can be computed at reduced cost. The MRRR algorithm (MRRR = Multiple Relatively Robust Representations) is a clever variant of inverse iteration without the need for reorthogonalization. stegr, the current version of MRRR in LAPACK 3.0, does...

We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on the complex spectral parameter λ and on the vector of real physical parameters p. We study perturbations of semi-simple multiple eigenvalues as well as pertu...

A method of speech enhancement using microphonearray signal processing based on the subspace method is proposed and evaluated in this paper. The method consists of the following two stages corresponding to the different types of noise. In the first stage, less-directional ambient noise is reduced by eliminating the noise-dominant subspace. It is realized by weighting the eigenvalues of the spat...

We developed a procedure of reducing the number of vertices and edges of a given tree, which we call the " tree simplification procedure, " without changing its topological information. Our motivation for developing this procedure was to reduce computational costs of graph Laplacian eigenvalues of such trees. When we applied this procedure to a set of trees representing dendritic structures of ...

Based on Lyapunov-exponent generation and the Gram-Schimdt orthogonalization, analysis and design of some anti-controlled higher-dimensional hyperchaotic systems are investigated in this paper. First, some theoretical results for Lyapunov-exponent generating algorithms are proposed. Then, the relationship between the number of Lyapunov exponents and the number of positive real parts of the eige...

We present a new approach to calculating time eigenvalues of the neutron transport operator (also known as α eigenvalues) by extending dynamic mode decomposition (DMD) allow for nonuniform steps. The method, called variable (VDMD), is shown be accurate when computing systems that were infeasible with DMD due large separation in timescales (such those occur delayed supercritical systems). an inf...

Existence of eigenvalues yielding single and multiple positive solutions for a system of higher order fractional differential equations along with boundary conditions is established. The results are obtained by the use of a Guo-Krasnosel’skii fixed point theorem in cones.

A deeation procedure is introduced that is designed to improve the convergence of an implicitly restarted Arnoldi iteration for computing a few eigenvalues of a large matrix. As the iteration progresses the Ritz value approximations of the eigenvalues of A converge at diierent rates. A numerically stable scheme is introduced that implicitly deeates the converged approximations from the iteratio...