Toeplitz matrisler ve onlarin numerik spektral özellikleri

In this study, we investigate the eigenvalues of a non-hermitian Toeplitz matrix A. These are usually highly sensitive to perturbations,having condition numbers that increase exponentially with the dimension N. An equivalent statement is that the resolvent (zI - A)^{ - 1} of a Toeplitz matrix may be much larger in norm than the eigenvalues alone would suggest-exponentially large as a function of N, even when z is far from the spectrum. Because of these facts, the meaningfulness of the eigenvalues of non-hermitian Toeplitz matrices for any but the most theoretical purposes should be considered suspect. In many applications it is more meaningful to investigate the varepsilon-pseudoeigenvalues.In the second part of study we investigate the pseudospectra of Linear Operators and analyzes the pseudospectra of Toeplitz matrices, and in particular relates them to the symbols of the matrices and thereby to the spectra of the General Toeplitz matrices. Our results are reasonably complete in the triangular case, and preliminary in the cases of non-triangular Toeplitz matrices with smoothly varying coefficients.This study presents computed examples of pseudospectrum for the General Toeplitz matrices with using Mathematica and Matlab programming, and applications in numerical analysis.Keywords: Eigenvalue, eigenvector, pseudoeigenvalue, spectrum, pseudospectrum, Toeplitz matrix.