On the use of Hahn's asymptotic formula and stabilized recurrence for a\n fast, simple, and stable Chebyshev--Jacobi transform
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Bibliographic record
Abstract
We describe a fast, simple, and stable transform of Chebyshev expansion\ncoefficients to Jacobi expansion coefficients and its inverse based on the\nnumerical evaluation of Jacobi expansions at the Chebyshev--Lobatto points.\nThis is achieved via a decomposition of Hahn's interior asymptotic formula into\na small sum of diagonally scaled discrete sine and cosine transforms and the\nuse of stable recurrence relations. It is known that the Clenshaw--Smith\nalgorithm is not uniformly stable on the entire interval of orthogonality.\nTherefore, Reinsch's modification is extended for Jacobi polynomials and\nemployed near the endpoints to improve numerical stability.\n
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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