Paper Info
Title
Reconstruction Algorithms for Sums of Affine Powers.
Abstract
A sum of affine powers is an expression of the form f(x) = s∑/i=1 αi (x - ai)ei. Although quite simple, this model is a generalization of two well-studied models: Waring decomposition and Sparsest Shift. For these three models there are natural extensions to several variables, but this paper is mostly focused on univariate polynomials. We propose algorithms that find the smallest decomposition of f in the first model (sums of affine powers) for an input polynomial f given in dense representation. Our algorithms only work in situations where the smallest decomposition is unique, and we provide conditions that guarantee the uniqueness of the smallest decomposition.
Year
DOI
Venue
2017
10.1145/3087604.3087605
Journal of Symbolic Computation
DocType
Volume
Citations 
Conference
abs/1607.05420
2
PageRank 
References 
Authors
0.47
10
3
Name
Order
Citations
PageRank
Ignacio García-Marco162.66
Pascal Koiran2919113.85
Timothée Pecatte3162.89