Nonstandard Wavelet Matrix Multiplication
y = NonStdWaveMult(NS,x,L,qmf)
Matrix in Nonstandard form
vector in natural basis
Coarsest Resolution level of Wavelet Transform
quadrature mirror filter (orthogonal)
Result of nonstandard multiplication
If M is a matrix, there are two ways to compute y = M*x. The first is to use MATLAB to do the product as just written. This algorithm works in order n^2 time, where n is the problem size.
The second is to transform both the matrix and vector to their nonstandard forms and multiply the nonstandard forms. If the matrix is sparse in nonstandard form, this can be an order n algorithm.