Wavelet Methods - Computational Methods for Quantitative Finance - page 175

Fig. 12.6 Convergence rate
for the variance gamma
model ( top ) and elapsed time
(in seconds) to solve the
linear systems ( bottom )

(N − 2 ) but only

hp -dG approximation we still obtain the optimal convergence rate O

(N 3 ) . need (up to log terms) O (N) seconds to solve the linear systems instead of O

12.4 Further Reading

For a general introduction to wavelets, we refer to Daubechies [52], whereas a fo-
cus on the numerical solution of operator equations by wavelet methods can be
found, e.g. in Cohen [38], Dahmen [50], Urban [155], and the references therein.
The wavelet compression of the stiffness matrix corresponding to singular integral
operators (similar to the jump operator of Lévy processes) is discussed in, e.g. Dah-
men [51] and in von Petersdorff and Schwab [158].