Courses / ActivitiesThe optimal iterative algorithm to solve nonlinear algebraic equations
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An iterative algorithm based on the concept of best vector is proposed to solve a system of nonlinear algebraic equations (NAEs): F(x)=0. In terms of the residual vector F and a monotonically increasing positive function Q(t) of a time-like variable t, we define a future cone in the Minkowski space, wherein the discrete dynamics of the proposed algorithm evolves. A new method to approximate the best vector is developed, and we find a critical value of the weighting parameter in the descent vector for an iterative algorithm to solve x from the NAEs, which we label as the best vector optimal iterative algorithm (BVOIA). Some numerical examples are used to validate the performance of the BVOIA: a very fast convergence rate in finding the solution is observed.
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Chein-Shan Liu
2012-03-14
15:00:00 - 17:00:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
An iterative algorithm based on the concept of best vector is proposed to solve a system of nonlinear algebraic equations (NAEs): F(x)=0. In terms of the residual vector F and a monotonically increasing positive function Q(t) of a time-like variable t, we define a future cone in the Minkowski space, wherein the discrete dynamics of the proposed algorithm evolves. A new method to approximate the best vector is developed, and we find a critical value of the weighting parameter in the descent vector for an iterative algorithm to solve x from the NAEs, which we label as the best vector optimal iterative algorithm (BVOIA). Some numerical examples are used to validate the performance of the BVOIA: a very fast convergence rate in finding the solution is observed.