The random product homotopy and deficient polynomial systems
Numerische Mathematik
Coefficient-parameter polynomial continuation
Applied Mathematics and Computation
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
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Geometric constraint problem is equivalent to the problem of solving a set of nonlinear equations substantially. Nonlinear equations can be solved by classical Newton-Raphson algorithm. Path tracking is the iterative application of Newton-Raphson algorithm. The Homotopy iteration method based on the path tracking is appropriate for solving all polynomial equations. Due to at every step of path tracking we get rid off the estimating tache, and the number of divisor part is less, so the calculation efficiency is higher than the common continuum method and the calculation complexity is also less than the common continuum method.