A global root-finding method for high dimensional problems - Mathematics > Numerical AnalysisReport as inadecuate




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Abstract: A method to solve the problem fx = 0 efficiently on any n-dimensionaldomain Omega under very broad hypoteses is proposed. The position of the rootof f, assumed unique, is found by computing the center of mass of anOmega-shaped object having a singular mass density. It is shown that althoughthe mass of the object is infinite, the position of its center of mass can becomputed exactly and corresponds to the solution of the problem. The exactanalytical result is implemented numerically by means of an adaptive MonteCarlo sampling technique which provides an exponential rate of convergence. Themethod can be extended to functions with multiple roots, providing an efficientautomated root finding algorithm.



Author: Fabrizio Castellano

Source: https://arxiv.org/







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