A Numerical Model for the Construction of Finite Blaschke Products with Preassigned Distinct Critical Points

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Interna författare/redaktörer


Publikationens författare: Christer Glader, Ray Pörn
Förläggare: arXiv.org
Publiceringsår: 2018


Abstrakt



We present a numerical model for determining a finite Blaschke product of degree n+1nhaving nnpreassigned distinct critical points z1,...,znin the complex (open) unit disk D. The Blaschke product is uniquely determined up to postcomposition with conformal automorphisms of D.
The proposed method is based on the construction of a sparse nonlinear
system where the data dependency is isolated to two vectors and on a
certain transformation of the critical points. The efficiency and
accuracy of the method is illustrated in several examples.


Senast uppdaterad 2019-18-10 vid 03:57