Both the theoretical and practical investigations of various dynamical systems need to extend the definitions of various functions defined on the real axis to the set of matrices. To this end one uses mainly three methods which are based on 1) the Jordan canonical forms, 2) the polynomial interpolation, and 3) the Cauchy integral formula. All these methods give the same result, say g(A), when t...

We propose an approach for the simultaneous bounding box estimation of multiple organs in volumetric CT images. Local eigen-organ spaces are constructed for different types of training organs, and a global eigen-space, which describes the spatial relationships between the organs, is also constructed. Each volume of interest in the abdominal CT image is projected into the local eigen-organ space...

We investigate the expressive power of MATLANG, a formal language for matrix manipulation based on common matrix operations and linear algebra. The language can be extended with the operation inv of inverting a matrix. In MATLANG + inv we can compute the transitive closure of directed graphs, whereas we show that this is not possible without inversion. Indeed we show that the basic language can...

Deformations in handwritten characters have category-dependent tendencies. In this paper, the estimation and the utilization of such tendencies called eigen-deformations are investigated for the better performance of elastic matching based handwritten character recognition. The eigen-deformations are estimated by the principal component analysis of actual deformations automatically collected by...

We survey and extend the recent progress in polynomial root-finding based on reducing the problem to eigen-solving for highly structured generalized companion matrices. In particular we cover the selection of the eigen-solvers and the matrices and the resulting benefits based on exploiting matrix structure. No good estimates for global convergence of the basic eigen-solvers have been proved, bu...

By introducing the generalized master function of order up to four together with corresponding weight function, we have obtained all quasi-exactly solvable second order differential equations. It is shown that these differntial equations have solutions of polynomial type with factorziation properties, that is polynomial solutions Pm(E) can be factorized in terms of polynomial Pn+1(E) for m ≥ n+...

In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which express the generalized La-guerre expansion coecients for the moments of the derivatives of any dierentiable function in termsof th...

This search engine allows users to quickly obtain information from networks. Traditional search engines can only search the data of modal characters. To solve this problem, Image Comparison Search Engine (ICSE) makes use of “Fractal Image processing “to create a database using image Eigen values. When a user input is an image query, this system will generate image Eigen value data, compare this...