| EPSRC Reference: |
GR/L41639/01 |
| Title: |
APPROXIMATION ON SPHERES |
| Principal Investigator: |
Levesley, Professor J |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
University of Leicester |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
17 February 1997 |
Ends: |
16 February 1999 |
Value (£): |
8,000
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Summary on Grant Application Form |
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In many applied sciences it is becoming increasingly important to be able to approximate functions on both the whole of the sphere and portions of the sphere. We wish to consider global approximation on the sphere using the interpolation and Fourier methods. Using the results (4) on optimal interpolation and approximation on the sphere, we will compare the convergence rates of the methods we develop with the best possible rates, in order to give an estimate of their efficacy. For interpolation we will use sk-splines. We will give representations for spline interpolants, at the atlas points, using translates of a fixed kernal. We will then use the tools of harmonic analysis to deduce error estimates for such an interpolation process. We will employ the results of (9) to extend the results of Ragozin (12) and Kamzolov (3), who considered the approximation of smooth functions using Fourier series. We will then consider the generation of approximations by discrete Fourier transform, and investigate the use of the fast transform methods of Driscoll and Healy (1) for practical computation.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.le.ac.uk |