Quadratic Approximation And Nonlinear Optimization Collinear Tone Than The Method

Using the conic function model local approximation, W.CDavidon(1980) proposed a class of iterative algorithms with modified matrix combining function value, furthermore under the theory D.C.Sorensen has used local quadratic approximation method ,then applying collinear scaling idea improving on the above algorithm and generalizing it , getting a class of collinear scaling algorithm, unifying former quasi-Newton. In the paper, using local quadratic approximation method, the first, constructing the new collinear scaling gene ,getting a class of the new collinear scaling algorithm with briefness and numerical stability,., we discusses some properties of the algorithm and its local linearconvergence,Q-superlinear convergence and the whole convergence; secondly we have made numerical experimentation and numerical analysis; the last ,we have done much discussion for collinear scaling idea and given the several new collinear scaling algorithm.