A nonlinear Chaikin-based binary subdivision scheme. (English) Zbl 1528.65013
Summary: In this work we introduce and analyze a new nonlinear subdivision scheme based on a nonlinear blending between Chaikin’s subdivision rules and the linear 3-cell subdivision scheme. Our scheme seeks to improve the lack of convergence in the uniform metric of the nonlinear scheme proposed in [S. Amat et al., S\(\vec{\text{e}}\)MA J. 60, 75–92 (2012; Zbl 1260.94005)], where the authors define a cell-average version of the PPH subdivision scheme [S. Amat et al., Found. Comput. Math. 6, No. 2, 193–225 (2006; Zbl 1106.41001)]. The properties of the new scheme are analyzed and its performance is illustrated through numerical examples.
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