A gradient-weighted, data-dependent polynomial norm makes approximate border basis computation invariant to data scaling and more stable to perturbations than coefficient normalization.
Approximate computation of zero-dimensional polynomial ideals
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Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation
A gradient-weighted, data-dependent polynomial norm makes approximate border basis computation invariant to data scaling and more stable to perturbations than coefficient normalization.