Matrix-Vector Multiplication in Adaptive Wavelet Methods
Dana Černá, Václav Finěk, George Venkov, Ralitza Krumova Kovacheva, Vesela Pasheva · AIP conference proceedings · 2011
Wavelet based methods are an established tool in signal and image processing and a promising tool for the numerical solution of operator equations. They have namely some interesting properties which may provide an advantage over classical methods. It is well‐known fact that representations of smooth functions and also representations of a wide class of operators are sparse in wavelet coordinates. Further advantage of wavelet methods consists in the existence of a diagonal preconditioner. The condition number of the preconditioned stiffness matrices does not depend on the size of matrices. Although the stiffness matrices in wavelet coordinates are only quasi sparse, an approximate multiplication of these matrices with given sparse vectors can be performed in the linear complexity. These are crucial parts to design efficient adaptive wavelet schemes. In this contribution, we focus on biorthogonal spline wavelets and we compare different approximate matrix‐vector multiplication techniques.