**MSC:**- 41A10 Approximation by polynomials, {For approximation by trigonometric polynomials, See 42A10}
- 15A23 Factorization of matrices

calculated recursively, and the refinement matrices are given explicitely.

Moreover, the eigenvectors of the transposed refinement matrices are

constructed, whereas the eigenvectors of the refinement matrices

themselves can be determined by a theorem of Micchelli and Prautzsch.