Stochastic Volatility Models with Jumps - Computational Methods for Quantitative Finance - page 240

Fig. 15.1 Condition number
for hat functions ( top )and
wavelets with preconditioning
( bottom )

(L 5 ) GMRES iterations , the fully discrete Galerkin scheme
with incomplete GMRES gives

using in each time step O

p − 1

CN − s
L

U dG (T ) ( log 2 N L ) (d − 1 )s + ε ,s

u(T ) − L 2 (G) ≤ := p − 1 +

1 . dp −

Remark 15.4.8 The numerical experiments in the examples below show that the
convergence rate of Theorem 15.4.7 is likely not optimal. Indeed, the experiments
suggest that the error measured in L 2 satisfies the same estimate as the sparse grid
projector P L (at least for the wavelets of Example 12.1.1), i.e.

CN − p
L

U dG (T ) ( log 2 N L ) (d − 1 )(p + 1 / 2 ) + ε u(T ) − L 2 (G) ≤ ;

compare with Theorem 13.1.2.