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Abstract. The paper concerns numerical algorithms for solving the Beltrami equation fz(z) = µ(z)fz (z) for a compactly supported µ.First, we study an efficient algorithm that has been proposed in the literature, and present its rigorous justification. We then propose a different scheme for solving the Beltrami equation which has a comparable speed and accuracy, but has the virtue of a greater simplicity of implementation.

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