We consider a class of matrices that are of interest to numerical applications and are large, sparse, but not symmetric or diagonally dominant. We give a criterion for the existence of (and we actually construct) the inverse matrix in terms of powers of a "small" matrix. We use this criterion to find that the spectral radius of the Jacobi iteration matrix, corresponding to a block tridiagonal p...

In this paper, an application to the approximation by wavelets has been obtained by using matrix-Cesàro (Λ · C1) method of Jacobi polynomials. The rapid rate of convergence of matrix-Cesàro method of Jacobi polynomials are estimated. The result of Theorem (6.1) of this research paper is applicable for avoiding the Gibbs phenomenon in intermediate levels of wavelet approximations. There are majo...

A selfadjoined block tridiagonal matrix with positive definite blocks on the off-diagonals is by definition a Jacobi matrix with matrix entries. Transfer matrix techniques are extended in order to develop a rotation number calculation for its eigenvalues. This is a matricial generalization of the oscillation theorem for the discrete analogues of Sturm-Liouville operators. The three universality...

first riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. an analytical approximation of the solution of nonlinear differential riccati equation is investigated using the adomian decomposition method. an application in optimal control is presented. the solution in different order of approximations and different methods of approximat...

We study spectrum inclusion regions for complex Jacobi matrices which are compact perturbations of real periodic Jacobi matrix. The condition sufficient for the lack of discrete spectrum for such matrices is given.

Abstract. By using cutting strips and transformations on outside decompositions of a skew diagram, we show that the Giambelli-type matrices for a given skew Schur function are stably equivalent to each other over symmetric functions. As a consequence, the Jacobi-Trudi matrix and the transpose of the dual Jacobi-Trudi matrix are stably equivalent over symmetric functions. This leads to an affirm...

One sided block Jacobi algorithm for the singular value decomposition (SVD) of matrix can be a method of choice to compute SVD efficiently and accurately in parallel. A given matrix is logically partitioned into block columns and is subjected to an iteration process. In each iteration step, for given two block columns, their Gram matrix is generated, its symmetric eigenvalue decomposition (EVD)...

| In a note at the end of his paper Recherches sur les fractions continues, Stieltjes gave a necessary and suucient condition when a continued fraction is represented by a meromorphic function. This result is related to the study of compact Jacobi matrices. We indicate how this notion was developped and used since Stieltjes, with special attention to the results by M. G. Krein. We also pay atte...

We discuss a new method for the iterative computation of a portion of the singular values and vectors of a large sparse matrix. Similar to the Jacobi-Davidson method for the eigenvalue problem, we compute in each step a correction by (approximately) solving a correction equation. It is shown that this JDSVD method can be seen as an accelerated (inexact) Newton scheme. We compare the method with...

Abstract. By using cutting strips and transformations on outside decompositions of a skew diagram, we show that the Giambelli type matrices of a skew Schur function are stably equivalent to each other over symmetric functions. As a consequence, the Jacobi-Trudi matrix and the dual Jacobi-Trudi matrix are stably equivalent over symmetric functions. This gives an affirmative answer to an open pro...