Fast algorithms for adaptive free knot spline approximation using nonuniform biorthogonal spline wavelets

New algorithms for fast wavelet transforms with biorthogonal spline wavelets on nonuniform grids are presented. In contrast 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.