The Promotion Of Coordinate Relaxation Algorithm

We propose a promotion of coordinate relaxation algorithm:xk+1=xkwkt1kp1k, to solve the nonlinear equations F(x)=0,x∈D,Where F:D*(?)R"→R" is a nonlinear mapping. There are 3 results in the paper:1 when F is a non-gradient mapping and ik is N-circle, under appropriate condition, we prove the global convergence of the algorithm.2 when F is a non-gradient mapping and ik is not N-circle, under appropriate condition, we prove the semi-local convergence of the algorithm.3 when F is a non-gradient mapping and ik is not N-circle, under appropriate condition, we prove the global convergence of the algorithm.