Lothar Berg, Gerlind Plonka
Refinement of Vectors of Bernstein Polynomials
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 50, 19-30 (1997)

MSC:

41A10 Approximation by polynomials, {For approximation by trigonometric polynomials, See 42A10}

15A23 Factorization of matrices

Abstract: For the case of Bernstein polynomials, the refinement mask is
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.

Keywords: Approximation by polynomials; Factorization of matrices; Eigenvalues, singular values and eigenvectors