With A Function Value Of The Multi-step Quasi-newton Method

Based on the quasi-newton algorithm, multi-step quasi-newton method utilizes interpolated polynomials which is determined by the previous m iterations, to assist solution updating in the next iteration step, thus reducing iteration steps and improving computational efficiency effectively. In the meanwhile, the single-step version algorithm is being researched as well, such as Zhang's quasi-newton method using function value.In this paper, based on a survey of previous work in the literature, I proposed two kinds of modified multi-step quasi-newton method using function value. And compare their advantages and disadvantages with the previous algorithms. The results of numerical experiments show that the new methods perform better when used in middle and high dimension functions. And the second one has quicker convergent rate at high dimension. But the two new methods both haven't so much advantage in iteration efficiency compared with the previous methods. But we also know from the numerical experiments the first one performs better than the second one in iteration efficiency.