Some semi-discrete analogous of well known one-point family of iterative methods for solving nonlinear scalar equations dependent on an arbitrary constant are proposed. The new families give multi-point iterative processes with the same or higher order of convergence. The convergence analysis and numerical examples are presented.
The two matrix iterations X k+1 = I ∓ A * X −1 k A are known to converge linearly to a positive definite solution of the matrix equations X ± A * X −1 A = I, respectively, for known choices of X 0 and under certain restrictions on A. The convergence for previously suggested starting matrices X 0 is generally very slow. This paper explores different initial… (More)