Chein-Shan Liu1, Satya N. Atluri2
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.6, pp. 575-602, 2012, DOI:10.3970/cmes.2012.084.575
Abstract An iterative algorithm based on the concept of best descent vector u in x· = λu 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 descent vector is developed, and we find a critical value of the weighting parameter αc in the best descent vector u = αcF + BTF, where B = ∂F/∂x is the More >