| Title | Improving numerical accuracy of Grobner basis polynomial equation solvers |
| Authors | Martin Byröd, Klas Josephson, Karl Åström |
| Alternative Location | http://www.maths.lth.se/vis... |
| Alternative Location | http://dx.doi.org/10.1109/I..., Restricted Access |
| Publication | 2007 IEEE 11th International Conference onComputer Vision, vols 1-6 |
| Year | 2007 |
| Pages | 449 - 456 |
| Document type | Conference paper |
| Conference name | 11th IEEE International Conference on Computer Vision |
| Conference Date | Oct 14-21, 2007 |
| Conference Location | Rio de Janeiro, Brazil |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | IEEE Press |
| Abstract English | This paper presents techniques for improving the numerical stability of Grobner basis solvers for polynomial equations. Recently Grobner basis methods have been used succesfully to solve polynomial equations arising in global optimization e.g. three view triangulation and in many important minimal cases of structure from motion. Such methods work extremely well for problems of reasonably low degree, involving a few variables. Currently, the limiting factor in using these methods for larger and more demanding problems is numerical difficulties. In the paper we (i) show how to change basis in the quotient space Rx/I and propose a strategy for selecting a basis which improves the conditioning of a crucial elimination step, (ii) use this technique to devise a Grobner basis with improved precision and (iii) show how solving for the eigenvalues instead of eigenvectors can be used to improve precision further while retaining the same speed. We study these methods on some of the latest reported uses of Grobner basis methods and demonstrate dramatically improved numerical precision using these new techniques making it possible to solve a larger class of problems than previously. |
| ISBN/ISSN/Other | ISSN: 1550-5499 ISBN: 978-1-4244-1631-8 |
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