| EPSRC Reference: |
GR/T24036/01 |
| Title: |
Robust Computations in Geometric Modelling |
| Principal Investigator: |
Winkler, Dr J |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Department: |
Computer Science |
| Organisation: |
University of Sheffield |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 February 2005 |
Ends: |
31 January 2008 |
Value (£): |
71,785
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| EPSRC Research Topic Classifications: |
| Design & Testing Technology |
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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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Many problems in engineering and applied mathematics give rise to polynomial equations, and there exists a large body of theoretical knowledge about this class of equation. These equations are, however, difficult to solve numerically when the polynomial is of high degree and/or it has multiple (repeated) roots, in which case the established methods do not yield satisfactory answers. The theoretical reasons for this poor performance are known, and it was thought that they place a fundamental limit on the accuracy that can be obtained from the computational solution of these equations. This view, which had been maintained by numerical analysts for a long time, was challenged in 1972 by Professor Kahan of The Department of Mathematics at The University of California at Berkeley, USA. In particular, he performed theoretical analysis that provided deep insight into the fundamental cause of these problems. This insight refined substantially the previous explanation, and recent computational results by Professor Zeng (Northeastern Illinois University, USA) have confirmed the theory of Professor Kahan. Significantly, these results by Professor Zeng for the computational solution of polynomial equations are substantially better than the results obtained using established (classical) methods.The aim of the proposed research is the development of the work of Professor Kahan to a form that is appropriate for its incorporation into computeraided design (CAD) and geometric modelling (GM) systems. This development involves theoretical analysis, software development, computational testing, and a comparison with the established methods that are used for the solution of polynomial equations in CAD and GM systems. The excellent computational results obtained by Professor Zeng suggest that the potential improvement in the performance of CAD and GM systems is considerable, and the widespread industrial use of these systems implies that the benefits from the successful accomplishment of the proposed research are significant.
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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.shef.ac.uk |