Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases

Mark Giesbrecht, Erich Kaltofen, Wen-shin Lee
2003 Journal of symbolic computation  
We give a new class of algorithms for computing sparsest shifts of a given polynomial. Our algorithms are based on the early termination version of sparse interpolation algorithms: for a symbolic set of interpolation points, a sparsest shift must be a root of the first possible zero discrepancy that can be used as the early termination test. Through reformulating as multivariate shifts in a designated set, our algorithms can compute the sparsest shifts that simultaneously minimize the terms of
more » ... given set of polynomials. Our algorithms can also be applied to the Pochhammer and Chebyshev bases for the polynomials, and potentially to other bases as well. For a given univariate polynomial, we give a lower bound for the optimal sparsity. The efficiency of our algorithms can be further improved by imposing such a bound and pruning the highest degree terms.
doi:10.1016/s0747-7171(03)00087-7 fatcat:nrvwxfpd3bfirii5xubb6sl2eq