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## Jacobi matrices, orthogonal polynomials and Gauss quadrature An introduction and some results for the non-hermitian caseSeminario Dottorato - Stefano POZZA (Numerical Analysis) "Jacobi matrices, orthogonal polynomials and Gauss quadrature - An introduction and some results for the non-hermitian case" This seminar is divided in two parts. In the first one we will give an introduction to the matter. We will present the concept of orthogonal polynomials and we will focus on the properties of the Jacobi matrix linked to them. Then we will see their application for the approximation of integrals (Gauss quadrature). In the second part we will see how the first part can be extended to the non-hermitian case. In particular we will present formal orthogonal polynomials and we will see the spectral properties of a generally complex Jacobi matrix. This will lead us to some results about the extension of the Gauss quadrature in the complex plane. |