Non-linear families of projections on C[−1, 1]
Many approximation processes can be regarded as defining linear projections on a suitable normed linear space, usually the space of continuous functions on some closed interval of the real line. In this case the norm of the projection gives an estimate for how well the process will perform in practi...
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| Published in | Journal of approximation theory Vol. 30; no. 3; pp. 197 - 202 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.01.1980
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| Online Access | Get full text |
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| Summary: | Many approximation processes can be regarded as defining linear projections on a suitable normed linear space, usually the space of continuous functions on some closed interval of the real line. In this case the norm of the projection gives an estimate for how well the process will perform in practice. Numerical evidence shows that amongst ultraspherical projections, the Chebyshev projection (arising from the truncated Chebyshev series) does not have minimal norm. In this paper we demonstrate this fact analytically by deriving first some general principles, and then applying these to the Chebyshev projection. |
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| ISSN: | 0021-9045 1096-0430 |
| DOI: | 10.1016/0021-9045(80)90006-4 |