Fast Algorithms for Adaptive Free-Knot Spline Approximation Using Non-Uniform Biorthogonal Spline Wavelets
For researchers in numerical methods and circuit simulation, this work offers an efficient approach to adaptive spline approximation, though it is incremental in nature.
The paper presents fast wavelet transform algorithms for biorthogonal spline wavelets on nonuniform grids, enabling adaptive spline grid refinement and coarsening, with demonstrated performance in circuit simulation.
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.