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Chebyshev polynomials are not always optimal
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Fischer, Bernd Freund, Roland |
| Copyright Year | 1989 |
| Description | The problem is that of finding among all polynomials of degree at most n and normalized to be 1 at c the one with minimal uniform norm on Epsilon. Here, Epsilon is a given ellipse with both foci on the real axis and c is a given real point not contained in Epsilon. Problems of this type arise in certain iterative matrix computations and, in this context, it is generally believed and widely referenced that suitably normalized Chebyshev polynomials are optimal for such constrained approximation problems. It is shown that this is not true in general. Moreover, sufficient conditions are derived which guarantee that Chebyshev polynomials are optimal. Some numerical examples are also presented. |
| File Size | 446483 |
| Page Count | 18 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19900014692 |
| Archival Resource Key | ark:/13960/t3130s86z |
| Language | English |
| Publisher Date | 1989-04-01 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Points Mathematics Chebyshev Approximation Polynomials Iteration Ellipses Matrices Mathematics Foci Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
