A Univariate Polynomial Sparse Interpolation Algorithm Based On Exponential Analysis

Sparse interpolation of polynomials is not only of great significance in computational mathematics,but also in practical applications.In this paper,we discuss the problem of sparse interpolation of a univariate polynomial,and discuss how to recover the coefficients and degrees of nonzero terms of a sparse polynomial when the given interpolation condition is noisy.The problem of polynomial interpolation is regarded as an exponential analysis problem,and then a Sub-Nyquist exponential analysis method in the literature is applied to the polynomial sparse interpolation problem.In the numerical example,we compare with a widely accepted polynomial sparse interpolation algorithm in the current literature.The experimental results show that the proposed algorithm is effective and has some advantages.