Matrix multiplication can also be done using wavelet packets. The idea is to compute the wavelet packet analysis of the matrix (wpa2) and choose a basis for it (bestbas2, fixlvl2, wavbase2). Then the vector is transformed (wpa1) and the multiplication is done on the transformation side (wpmult); the basis chosen for the matrix determines which basis is eventually used for the vector and for the product. For more information see [13].
Example (continued from the previous section):
...
WPA = bestbas2(wpa2(A,h,g));
wpf = wpa1(f,h,g);
p = wps1(wpmult(WPA,wpf),h,g);
norm(p-A*f)
The error was
1.05801e-14
.