Numerical Algorithms for Zero Counting

Project: Research

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The problem of computing the number of solutions of a system of polynomial equations has recently been shown to be complete in a complexity class of counting problems. Symbolic algorithms solving this problem have been designed in the last few decades whose complexity is exponential (polynomial if an exponential number of processors are allowed to work in parallel). Like most symbolic algorithms, the behaviour of those just mentioned in terms of accuracy under the presence of round-off errors is rather bad.In contrast with the above, one could expect that the accuracy of a numerical algorithm would be better. But no such numerical algorithm has been developed for counting solutions of polynomial systems. The objective of this project is to design one.


Project number7002106
Grant typeSRG
Effective start/end date1/04/079/09/09