 
Summary: Adaptive Calculation of Variable Coefficients
Elliptic Differential Equations via Wavelets
Amir Averbuch1
, Leonid Beliak2
, Moshe Israeli2
1
School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978
Israel
2
Faculty of Computer Science, Technion Israel Institute of Technology
Haifa 32000, Israel
Abstract
We propose a solver for 1D strictly elliptic linear PDE's with noncon
stant coefficients of the form U  b(x)U = f(x). We combine a sparse
multiplication algorithm with a diagonally preconditioned conjugate gradient
(CG) method. We use sparse data structures to take advantage of the O(Ns)
complexity of the algorithm, where Ns is the number of significant coefficients
(i.e. above a certain threshold) required for a given accuracy.
We show that the usage of a sparse multiplication in wavelet space rather
than in the original physical space can speed up the performance of the sparse
