Friday, March 17, 2017 - 11:05
1 hour (actually 50 minutes)
Error-correcting decoding is generalized to multivariate sparse polynomial and rational function interpolation from evaluations that can be numerically inaccurate and where several evaluations can have severe errors (``outliers''). Our multivariate polynomial and rational function interpolation algorithm combines Zippel's symbolic sparse polynomial interpolation technique [Ph.D. Thesis MIT 1979] with the numeric algorithm by Kaltofen, Yang, and Zhi [Proc. SNC 2007], and removes outliers (``cleans up data'') by techniques from the Welch/Berlekamp decoder for Reed-Solomon codes. Our algorithms can build a sparse function model from a number of evaluations that is linear in the sparsity of the model, assuming that there are a constant number of ouliers and that the function probes can be randomly chosen.