Abstract A circle pattern is a configuration of circles with prescribed intersection angles in the complex plane $\mathbf{C}$. Given a analytic function with a finite critical points defined on a bounded simply connected region ${\mathit\Omega}\subset\mathbf{C}$, the techniques of branched circle patterns is used to construct the approximating solutions of $F$. It is proved that the sequence of approximating solutions converges uniformly on compact subsets of ${\mathit\Omega}$ to the analytic function $F$. This provides a new numeral method of computing analytic functions with critical points.
Received: 15 February 2014
Published: 10 June 2018
GUO Xiu-feng, LAN Shi-yi. Approximation of analytic functions with critical points by circle patterns. Applied Mathematics A Journal of Chinese Universities, 2014, 29(3): 352-360.
