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- W2910356254 abstract "We present an iterative root finding method for harmonic mappings in the complex plane, which is a generalization of Newton's method for analytic functions. The complex formulation of the method allows an analysis in a complex variables spirit. For zeros close to poles of $f = h + bar{g}$ we construct initial points for which the harmonic Newton iteration is guaranteed to converge. Moreover, we study the number of solutions of $f(z) = eta$ close to the critical set of $f$ for certain $eta in mathbb{C}$. We provide a Matlab implementation of the method, and illustrate our results with several examples and numerical experiments, including phase plots and plots of the basins of attraction." @default.
- W2910356254 created "2019-01-25" @default.
- W2910356254 creator A5017752084 @default.
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- W2910356254 date "2019-11-18" @default.
- W2910356254 modified "2023-10-18" @default.
- W2910356254 title "A Newton method for harmonic mappings in the plane" @default.
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- W2910356254 doi "https://doi.org/10.1093/imanum/drz042" @default.
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