Date of Award
Doctor of Philosophy
Dr. Philip Hsieh
Dr. Yousef Alavi
Dr. Paul Eenigenburg
Dr. Erik Schreiner
This work provides solid asymptotic representations, sharp error bounds and stable recurrence methods (both three term and two dimensional) for the Jacobi moments. These moments are currently used in several areas of numerical analysis (numerical integration, integral equations and boundary value problems).
A powerful representation theorem, due to H. Gingold, which uses the Jacobi moments is extended and analyzed. Applications of this theorem to multi-turning point problems and several other areas are given.
For a number of important problems in mathematical physics it is not possible to prove that the currently employed methods of solution converge, or are valid in any sense. In many such cases our methods may be shown to be uniformly convergent and numerically stable.
Kapenga, John A., "Jacobi Moments in Applied Mathematics with Computer Applications" (1986). Dissertations. 2285.