Ötelenmiş özdeğerler ve toeplitz matrislerin özellikleri

In this thesis we investigate the eigenvalues and pseudospectra of a nonhermitianToeplitz matrix A. These are usually highly sensitive to perturbations having conditionnumbers that increase exponentially with the dimension N. An equivalent statement isthat the resolvent R(z)=(zI-A)^{-1} of a Toeplitz matrix may be much larger in normthan the eigenvalue alone would be exponentially large as a function of N, even whenz is near to the spectrum. Because of these facts, the meaningfulness of the eigenvaluesof nonhermitian Toeplitz matrices for any purposes should be considered suspect. In manyapplications it is more meaningful to investigate the varepsilon-pseudoeigenvalues.In the second part of the thesis we investigate the pseudospectra of Triangular ToeplitzMatrices and analyzes the pseudospectra of lower and upper triangular and in particularrelates them to the symbols of the matrices and theory to the spectra of the Triangular Toeplitz matrices. Our results are reasonablycomplete in the triangular case, and preliminary in the cases of nontriangular Toeplitz matrices, with smoothly varying coefficients.This study presents computed examples of pseudospectrum for Triangular ToeplitzMatrices with using Mathematica and Matlab, and applications in numerical analysis.