| Abstract: |  Many problems in computer vision lead to polynomial systems solving. Therefore, we need an easy way how to generate an efficient solver for each problem. On this purpose, the automatic generator has been presented. In this thesis, we improve the automatic generator so we will be able to generate more efficient and numerically stable solvers.
To improve the automatic generator we review and implement several methods used in the state of the art Groebner basis solvers. Especially, we focus on the F4 Algorithm by Jean-Charles Faugere. Solvers, generated by the automatic generator, can be sped up when efficient methods are used to work with sparse matrices. We describe and implement method which is based on matrix partitioning. This method significantly speeds up the Gauss-Jordan elimination of sparse matrices.
We demonstrate the enhancements of the automatic generator on several important minimal problems. We show that the solvers generated by the new automatic generator are faster and numerically more stable than the solvers generated by the old version of the automatic generator.
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