A matricial computation of rational quadrature formulas on the unit circle |
| |
Authors: | Adhemar Bultheel Maria-José Cantero |
| |
Institution: | (1) Department of Computer Science, K.U. Leuven, Leuven, Belgium;(2) Department of Applied Mathematics, University of Zaragoza, Zaragoza, Spain |
| |
Abstract: | A matricial computation of quadrature formulas for orthogonal rational functions on the unit circle, is presented in this paper. The nodes of these quadrature formulas are the zeros of the para-orthogonal rational functions with poles in the exterior of the unit circle and the weights are given by the corresponding Christoffel numbers. We show how these nodes can be obtained as the eigenvalues of the operator Möbius transformations of Hessenberg matrices and also as the eigenvalues of the operator Möbius transformations of five-diagonal matrices, recently obtained. We illustrate the preceding results with some numerical examples. |
| |
Keywords: | Orthogonal rational functions Para-orthogonal rational functions Szegő quadrature formulas M?bius transformations |
本文献已被 SpringerLink 等数据库收录! |