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Asymptotics of orthogonal polynomials and the numerical solution of ill-posed problems |
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| Authors: | Martin Hanke |
| Institution: | (1) Institut für Praktische Mathematik, Universität Karlsruhe, D-76128 Karlsruhe, Germany |
| Abstract: | The paper reviews the impact of modern orthogonal polynomial theory on the analysis of numerical algorithms for ill-posed problems. Of major importance are uniform bounds for orthogonal polynomials on the support of the weight function, the growth of the extremal zeros, and asymptotics of the Christoffel functions. |
| Keywords: | Ill-posed problems iterative methods rate of convergence fast decreasing polynomials Christoffel functions zeros of orthogonal polynomials Tricomi-Carlitz polynomials Lommel polynomials |
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