2007 IEEE 11th International Conference on Computer Vision 2007
DOI: 10.1109/iccv.2007.4408885
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Improving Numerical Accuracy of Gr�bner Basis Polynomial Equation Solvers

Abstract: strategy for selecting a basis which improves the conditioning of a crucial elimination step, (ii) use this technique to devise a Gröbner 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 Gröbner basis methods and demonstrate dramatically improved numerical precision using these new techniques making it possible to solve a large… Show more

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Cited by 42 publications
(91 citation statements)
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“…After the G-J elimination of the corresponding 31 × 50 matrix (in fact 31 × 46 matrix is sufficient thanks to removing columns that do not affect G-J elimination) all necessary polynomial are obtained and the action matrix M x (M y ) is created. Our generated solver results in a little bit smaller matrix than the solver proposed in [2].…”
Section: Six Point Focal Length Problemmentioning
confidence: 98%
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“…After the G-J elimination of the corresponding 31 × 50 matrix (in fact 31 × 46 matrix is sufficient thanks to removing columns that do not affect G-J elimination) all necessary polynomial are obtained and the action matrix M x (M y ) is created. Our generated solver results in a little bit smaller matrix than the solver proposed in [2].…”
Section: Six Point Focal Length Problemmentioning
confidence: 98%
“…More recently, another Gröbner basis solver to this problem was proposed in [2]. This solver uses only one G-J elimination of a 34×50 matrix and uses special technique for improving the numerical stability of Gröbner basis solvers based on changing the basis B.…”
Section: Six Point Focal Length Problemmentioning
confidence: 99%
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