New Methods For Solving Singular Problems

In this paper, some iterate methods for solving singular problem are studied. The main results are as followingAs the calculation of Chord method is cheap and it is easy to use with Matlab. Chord method is always attentioned. The null space of one dimension had been studied. However, it is discommodious for us to use in many fields. In this paper, the convergence of Chord method is given. With the help of several lemmas, the error estimation is obtained. The rate of convergence of Chord method is slow, in order to conquer the disadvantage, the improved iterate scheme is given on the premise of few addition calculations, the rate of convergence of chord method is more quickly and the numerical example is given.Many methods are used to solve nonlinear problems, their rate of convergence is quick, for example, Newton-moser method, King-werner method, they are attentioned widely because of the quick rate of convergence. While these methods are used to solve singular problems, the rate of convergence is slow, it is discommodious for us to solve practical problems. According to the characters of general iterate schemes, in this paper, improved schemes are given. On the premise of few addition calculations, the rate of convergence is quicker.In this paper, Newton-Moser method, King-Werner method and quasi-Newton method are taken as examples and the improved methods are given to solve singular problems. The rate of convergence is slow before being improved, so their advantages are lose. The rate of convergence is quicker after being improved. The practicability of improved scheme is obvious. On the premise of few addition calculations, the new iterate schemes are constructed that greatly accelerate the rate of convergence, which have been studied in this paper. The expected goals in this paper are achieved.