A Class Of Iterative Methods For Solving Equations And Its Applications

When we make use of mathematical tools to research social phenomena and natural phenomena, or to resolve the engineering and other problems, a lot of problems can be ended up with solving the equation f(x) = 0. The iterative method is an important method to solve those equations f(x) = 0. In the first place, by means of Newton iterative function, the iterative function of Newton's method to handle the problem of multiple roots and the Halley iterative function, we give a class of iterative formulae for solving equations in one variable in this thesis and show its convergent order is at least quadratic. In the next place, we discuss the issues on stopping criteria of algorithms in the iteration procedures for root-finding problems.The whole thesis is divided into four parts.The first one is the fundamental theory that can be used in the thesis. It focuses on basic conceptions and study background about iterative method. After review of some classical iterative methods, we deduce detailedly Halley iterative formula by means of Thiele's continued fraction and Pade approximation respectively.The second one gives a class of iterative methods for solving equations. This part can be regarded as the key element of the thesis. We discuss how to construct the iterative schemes and ensure its convergence. Considering that derivatives can be approximated by divided differences, we get some other iterative formulae that avoid computing derivatives.The third part discusses Stopping Criteria of algorithms in the iteration procedures for root-finding problems. This part can be considered as another key element of the thesis. The deficiency is discussed of current stopping criterion of the iterative algorithm for solving root-finding problems, and some new united stopping criteria are presented. Numerical experiments show that these stopping criteria are effective.The last part involves applications of the iterative method in the field of CAGD. We put forward an algorithm for computing the intersection of a spiral curve with a plane.