For a given real n n matrix A and initial vectors v 1 and w 1 , we examine the sensitivity of the tridiagonal matrix T and the biorthogonal sets of vectors of the Lanczos reduction to small changes in A, v 1 and w 1. We also consider the sensitivity of the developing Krylov subspaces.

In this paper an efficient Algorithm based on Zadeh's extension principle has been investigated to approximate fuzzy solution of two-point fuzzy boundary value problems, with fuzzy boundary values. We use finite difference method in term of the upper bound and lower bound of $r$- level of fuzzy boundary values. The proposed approach gives a linear system with crisp tridiagonal coefficients matr...

We study the rate of convergence of Wilkinson’s shift iteration acting on Jacobi matrices with simple spectrum. We show that for AP-free spectra (i.e., simple spectra containing no arithmetic progression with 3 terms), convergence is cubic. In order 3, there exists a tridiagonal symmetric matrix P0 which is the limit of a sequence of a Wilkinson iteration, with the additional property that all ...

Physicists in the 70’s starting with ’t Hooft established that the number of suitably labeled planar maps with prescribed vertex degree distribution can be represented as the leading coefficient of the 1 N -expansion of a joint cumulant of traces of powers of a standard N-by-N GUE matrix. Here we undertake the calculation of this leading coefficient in a different way, namely, after first tridi...

Double Toeplitz (DT) codes are with a generator matrix of the form (I,T) T matrix, that is to say constant on diagonals parallel main. When tridiagonal and symmetric we determine its spectrum explicitly by using Dickson polynomials, deduce from there conditions for code be LCD. Using special concatenation process, construct optimal or quasi-optimal examples binary ternary LCD DT over extension ...

Computation of the eigenvalues of a symmetric tridiagonal matrix is a problem of great relevance. Many linear algebra libraries provide subroutines for solving it. But none of them is oriented to be executed in heterogeneous distributed memory multicomputers. In this work we focus on this kind of platforms. Two different load balancing schemes are presented and implemented. The experimental res...