Generalized Gauss-Radau and Gauss-Lobatto quadrature formulae

In this thesis we first study Gauss-Radau and Gauss-Lobatto quadrature formulae having end points of multiplicity 2 for the weight functions of Chebyshev type. A detailed study of the underlying orthogonal polynomials is given. In the case of any of the four Chebyshev-type weight functions the coefficients in the boundary terms are explicitly identified as rational functions in the number n of interior quadrature nodes. We also give an analytic treatment of the remainder term of generalized Gauss-Radau and Gauss-Lobatto quadrature rules. The respective kernels in the contour integral representation of the remainder are worked out in detail. Then a detailed study is undertaken as to the location on the elliptic contour where the kernel attains its maximum modulus. Finally, the Kronrod extensions of generalized Gauss-Radau and Gauss-Lobatto quadrature formulae are studied. We establish expansion formulas for the respective Stieltjes polynomials in terms of Chebyshev polynomials and obtain explicit expressions for the weights corresponding to the end points.