Sparse Interpolation Problems
2015-02-06 13:30 - 14:20
Room 304, Mathematics Research Center Building (ori. New Math. Bldg.)
Some results on the number of solutions of a special polynomial system arising from sparse interpolation problems with equally spaced sampling and then based on the coefficient parameter homotopy method, an efficient algorithm is proposed. Furthermore, the sparse interpolation problems with equally spaced sampling with missing data, for which the classical Prony method does not work, is considered. Such a problem concerns solving a polynomial system which is more complicated than that in the case without data missing. Properties of this polynomial system are investigated for some interesting cases. For some special cases, the numbers of isolated solutions for generic data are accurately estimated and, for some other cases, a conjecture on the numbers of solutions is proposed. And then, based on the coefficient parameter homotopy method, an efficient algorithm, in which only a few number of paths need to be traced, is proposed. Preliminary numerical tests show that the proposed algorithm is promising.