Border basis computation with gradient-weighted normalization. (arXiv:2101.00401v4 [cs.SC] UPDATED)

Normalization of polynomials plays a vital role in the approximate basis
computation of vanishing ideals. Coefficient normalization, which normalizes a
polynomial with its coefficient norm, is the most common method in computer
algebra. This study proposes the gradient-weighted normalization method for the
approximate border basis computation of vanishing ideals, inspired by recent
developments in machine learning. The data-dependent nature of
gradient-weighted normalization leads to better stability against perturbation
and consistency in the scaling of input points, which cannot be attained …

arxiv computation gradient normalization