| EPSRC Reference: |
GR/S87461/01 |
| Title: |
Series Summation and Ranom Continued Factions. |
| Principal Investigator: |
Tourigny, Dr Y |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
University of Bristol |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 October 2004 |
Ends: |
31 December 2007 |
Value (£): |
134,594
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| EPSRC Research Topic Classifications: |
| Continuum Mechanics |
Numerical Analysis |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Describe the proposed research using (about 200) words geared to the non-specialist reader.The problem of computing the sum of an infinite series is fundamental in applied mathematics, where solutions of difficult nonlinear problems are often sought as expansions in powers of some small parameters. The project seeks to quantifyand predict the performance of some widely used summation methods when they are applied to large classes of series. The approach will build on recent work by the principal investigator andhis collaborators and exploit a profound analogy between series summation and continued fractions. This novel approach brings together ideas from diverse areas: numerical analysis, number theory, dynamical systems and probability theory. A certain map on classes of series will be associated with the summation method, and the typical performance of the method for this class will be deduced from the explicit (or approximate) knowledge of a suitable invariant measure. Another aim will be to study some long standing problems of fluid dynamics by use of series summation methods. One of the applications is directly relevant to one of the Clay Institute's Millenium Prize problems on the long-time existence of a solution of the incompressible Euler equations.
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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.bris.ac.uk |