A Three-Dimensional Analogue to the Method of Bisections for Solving Nonlinear Equations

Abstract

This paper deals with a three-dimensional analogue to the method of T bisections for solving a nonlinear system of equations F(X) = 9 = (0, 0, 0) , which does not require the evaluation of derivatives of F.We divide the original parallelepiped (Figure 2.1) into 8 tetrahedra (Figure 2.2), and then bisect the tetrahedra to form an infinite sequence of tetrahedra, whose vertices converge toZS such that FiZ) = 0.The process of bisecting a