Abstract
A triangulation of arbitrary refinement of grid sizes of (0, 1] × ℝn is proposed for simplicial homotopy algorithms for computing solutions of nonlinear equations. On each level the new triangulation, called theD 2-triangulation, subdivides ℝn into simplices according to theD 1-triangulation. We prove that theD 2-triangulation is superior to theK 2-triangulation andJ 2-triangulation in the number of simplices. Numerical tests show that the simplicial homotopy algorithm based on theD 2-triangulation indeed is much more efficient.
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Dang, C. TheD 2-triangulation for simplicial homotopy algorithms for computing solutions of nonlinear equations. Mathematical Programming 59, 307–324 (1993). https://doi.org/10.1007/BF01581250
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DOI: https://doi.org/10.1007/BF01581250