Exploiting p-Fold Symmetries for Faster Polynomial Equation Solving

Ask, Erik; Kuang, Yubin; Åström, Karl (2012). Exploiting p-Fold Symmetries for Faster Polynomial Equation Solving , 3232 - 3235. 21st International Conference on Pattern Recognition (ICPR 2012). Tsukuba, Japan: IEEE--Institute of Electrical and Electronics Engineers Inc.
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Conference Proceeding/Paper | Published | English
Ask, Erik ; Kuang, Yubin ; Åström, Karl
Mathematics (Faculty of Engineering)
Centre for Mathematical Sciences
Mathematical Imaging Group
ELLIIT: the Linköping-Lund initiative on IT and mobile communication
Research Group:
Mathematical Imaging Group
Numerous geometric problems in computer vision in-

volve the solution of systems of polynomial equations.

This is true for problems with minimal information, but

also for finding stationary points for overdetermined

problems. The state-of-the-art is based on the use of

numerical linear algebra on the large but sparse co-

efficient matrix that represents the expanded original

equation set. In this paper we present two simplifica-

tions that can be used (i) if the zero vector is one of

the solutions or (ii) if the equations display certain p-

fold symmetries. We evaluate the simplifications on a

few example problems and demonstrate that significant

speed increases are possible without loosing accuracy.
geometry ; algebra ; computer vision ; Polynomial equation solving
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