A practical application of information theoretic criteria is presented in this paper. Eigenvalue decomposition of the signal correlation matrix–based AIC, MDL and MIBS criteria are investigated and used for on–line estimation of time– varying parameters of harmonic signals in power systems.

The map which takes a square matrix to its tropical eigenvalue-eigenvector pair is piecewise linear. We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we also study the restriction of that cone decomposition to the subspace of skew-symmetric matrices.

In this paper we discuss how to design efficient Jacobi-like algorithms for eigenvalue decomposition of a real normal matrix. We introduce a block Jacobi-like method. This method uses only real arithmetic and orthogonal similarity transformations and achieves ultimate quadratic convergence. A theoretical analysis is conducted and some experimental results are presented.

In this paper the Adomian decomposition method is applied to the nonlinear SturmLiouville problem −y + y(t) = λy(t), y(t) > 0, t ∈ I = (0, 1), y(0) = y(1) = 0, where p > 1 is a constant and λ > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfuctions of the problem are demonstrated.

Beyn’s algorithm for solving nonlinear eigenvalue problems is given a new interpretation and a variant is designed in which the required information is extracted via the canonical polyadic decomposition of a Hankel tensor. A numerical example shows that the choice of the filter function is very important, particularly with respect to where it is positioned in the complex plane.

Modern communication, control, avionic, and radar systems require the use of computationally intensive algebraic operations for real-time high throughput filtering, estimation, tracking, direction-of-arrival, and localization purposes. In this overview paper, we first review some basic systolic array (SA) concept, then SA algorithms for digital filtering, recursive least-squares, QR decompositi...

In this paper we introduce a method for designing efficient Jacobi-like algorithms for eigenvalue decomposition of a real normal matrix. The algorithms use only real arithmetic and achieve ultimate quadratic convergence. A theoretical analysis is conducted and some experimental results are presented.

We consider the problem of writing an arbitrary symmetric matrix as the difference of two positive semidefinite matrices. We start with simple ideas such as eigenvalue decomposition. Then, we develop a simple adaptation of the Cholesky that returns a difference-of-Cholesky representation of indefinite matrices. Heuristics that promote sparsity can be applied directly to this modification.

Using QR-like decomposition with column pivoting and least squares techniques, we propose a new and ecient algorithm for solving symmetric generalized inverse eigenvalue problems, and give its locally quadratic convergence analysis. We also present some numerical experiments which illustrate the behaviour of our algorithm. Ó 1999 Elsevier Science Inc. All rights reserved. AMS classi®cation: 65...

Nonlinear spinor theory is fomulated in functional space. An eigenvalue equation for mesons is derived. The group theoretical reduction of this equation is performed, especially the angular momentum decomposition. For vector mesons it is solved in first Fredholm approximation. A solution corresponding to a physical particle is found contrary to earlier calculations. The calculated mass has the ...