Fast Algorithms for Adaptive Free-Knot Spline Approximation Using Non-Uniform Biorthogonal Spline Wavelets

TL;DR

This paper introduces fast algorithms for adaptive free-knot spline approximation using non-uniform biorthogonal spline wavelets, enabling efficient grid refinement and coarsening for applications like circuit simulation.

Contribution

It presents novel algorithms for wavelet transforms on nonuniform grids based on B-spline expansion techniques, not filter coefficients, improving adaptive spline approximation.

Findings

Algorithms outperform classical methods in efficiency

Numerical tests show effective adaptive spline approximation

Applicable to circuit simulation and other adaptive modeling

Abstract

New algorithms for fast wavelet transforms with biorthogonal spline wavelets on nonuniform grids are presented. In contrary to classical wavelet transforms, the algorithms are not based on filter coefficients, but on algorithms for B-spline expansions (differentiation, Oslo algorithm, etc.). Due to inherent properties of the spline wavelets, the algorithm can be modified for spline grid refinement or coarsening. The performance of the algorithms is demonstrated by numerical tests of the adaptive spline methods in circuit simulation.