İkinci dereceden operatör katsayılı polinomların özdeğer problemi ve pseudospektrum

In this study we investigate quadratic eigenvalue problem. It has extensive applications in engineering such as linear stability of flows in fluid mechanics, the dynamic analysis of mechanical systems in acoustics and signal processing.Our aim is to find spectrum points of quadratic pencil and investigate sensitivity of eigenvalues of quadratic pencil to perturbations. Eigenvalues of matrix pencil and eigenvalues of its factors are found and they are compared. Moreover, eigenvalues of quadratic pencil and eigenvalues of its linearization also their sensitivity are compared.In chapter two we will give general background for linearization and factorization. Pseudospectra notion for matrices can be extended to pseudospectra of quadratic matrix polynomial. Spectrum and pseudospectrum of matrix pencil are compared using factorization and linearization tecniques.In the last chapter we give computed examples for the spectrum and pseudospectrum of quadratic pencils. In our examples our matrix coefficients are choosen special matrices such as Hermitian, positive definite, Toeplitz etc? We use Mathematica programming to compute examples.Key words: Eigenvalue, eigenvector, quadratic eigenvalue problem, spectrum, pseudospectrum, positive definite matrix, Hermitian matrix, Toeplitz matrix.