Probabilistically Stable Numerical Sparse Polynomial Interpolation

We consider the problem of sparse interpolation of a multivariate black-box polynomial in floating-point arithmetic. That is, both the inputs and outputs of the black-box polynomial have some error, and all values are represented in standard, fixed-precision, floating-point arithmetic. By interpolating the black box evaluated at random primitive roots of unity, we give an efficient and numerically robust solution with high probability. We outline the numerical stability of our algorithm, as well as the expected conditioning achieved through randomization. Finally, we demonstrate the effectiveness of our techniques through numerical experiments.

• Type: Conference
• Year: 2006
• Where: DAGSTUHL
• Authors: Mark Giesbrecht, George Labahn, Wen-shin Lee
• Keywords: Black-box Polynomial, DAGSTUHL 2006, DAGSTUHL 2007, Floating-Point Arithmetic, Multivariate Black-box Polynomial