1 research outputs found
Sparse Interpolation With Errors in Chebyshev Basis Beyond Redundant-Block Decoding
We present sparse interpolation algorithms for recovering a polynomial with
terms from evaluations at distinct values for the variable when
of the evaluations can be erroneous. Our algorithms perform exact
arithmetic in the field of scalars and the terms can be standard
powers of the variable or Chebyshev polynomials, in which case the
characteristic of is . Our algorithms return a list of
valid sparse interpolants for the support points and run in
polynomial-time. For standard power basis our algorithms sample at points, which are fewer points than given by Kaltofen and Pernet in 2014. For Chebyshev basis our algorithms
sample at points, which are also
fewer than the number of points required by the algorithm given by Arnold and
Kaltofen in 2015, which has for and . Our method shows how to correct errors in a block of
points for standard basis and how to correct error in a block of
points for Chebyshev Basis.Comment: in IEEE Transactions on Information Theor