Alperts multi-wavelets from spline super-functions

For multi-wavelets generalized left eigenvectors of the matrix H _f a finite portion of down-sampled convolution matrix H determine the combinations of scaling functions that produce the desired spline or scaling function from which polynomials of desired degree can be reproduced. This condition is used to construct Alpert´s multi-wavelets with multiplicity two, three and four and with approximation orders two, three and four respectively. Higher-multiplicity Alpert multi-wavelets can also be constructed using this new method