Novel algorithms solving nonlinear equation in very large scope

Abstract

Two new algorithms used in large-scope solution are put forward to solve nonlinear equations which were not solved by some traditional methods. The initial value was arbitrarily chosen in very large scope. The convergence theorem of the algorithm was presented and proved. The computation is carried out by simple steepest descent rule without evaluation of the derivative evaluation of . Thus, computation time is saved. The specific examples showed that the proposed method can choose the initial value in very large scope, without the derivative evaluation, and less computation with high precision and rapid convergence.