The D2-triangulation for simplicial homotopy algorithms for computing solutions of nonlinear equations

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 the D2-triangulation, subdivides ℝⁿ into simplices according to the D1-triangulation. The paper proves that the D2-triangulation is superior to the K2-triangulation and J2-triangulation in the number of simplices. Numerical tests show that the simplicial homotopy algorithm based on the D2-triangulation indeed is much more efficient.