Computational fixed point theorems can be used to automatically verify existence and uniqueness of a solution to a nonlinear system of n equations in n variables ranging within a given region of n-space. Such computations succeed, however, only when the Jacobi matrix is nonsingular everywhere in this region. However, in problems such as bifurcation problems or surface intersection problems, the...

In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.

Indexing terms : Parallel algorithms, systolic arrays, matrix computation Jacobi-type matrix algorithms are mostly implemented on orthogonally connected processor arrays. In this letter, an alternative partitioning is described, resulting in a grid of hexagonally connected processors. This partitioning is shown to be over four times more efficient, as compared to the original configuration. Int...

Using spectral theory of unitary operators and the theory of orthogonal polynomials on the unit circle, we propose a simple matrix model for the following circular analogue of the Jacobi ensemble:

In this paper, we start with the quantum Hamilton-Jacobi approach and show that underlying complex pole evolution of Schr\"odinger equation is described by action in terms a random matrix. The wave function given matrix probability distribution function. literature known as famous Cole-Hopf Transformation.

We show that a unitary upper Hessenberg matrix with positive subdiago-nal elements is uniquely determined by its eigenvalues and the eigenvalues of a modiied principal submatrix. This provides an analog of a well-known result for Jacobi matrices.

The list of physically motivated urn models that can be solved in terms classical orthogonal polynomials is very small. It includes a model proposed by D. Bernoulli and further analyzed S. Laplace P. T. Ehrenfest eventually connected with the Krawtchouk Hahn polynomials. This connection was reversed recently case Jacobi where rather contrived, later simpler proposed. Here we consider an going J...

In the MUSIC approach for multiple emitter location, the array covariance matrix is a Hermite matrix. In order to realize the MUSIC approach, we have to do the work of eigenvalue-based decomposition of the Hermite matrix. This paper proves that the problem of Hermite matrix decomposition can be transformed into the problem of real symmetric matrix decomposition, and the article gives the detail...

.. ................................................................................................................... ix Chapter 1. Introduction ..................................................................................................1 Chapter 2. Background ..................................................................................................6 2.1. Matrix Compu...