Research on variable scale algorithm

This paper is mainly to study the calculation characteristics of different iterative matrices H(k+1) for different function types in the variable scale algorithm. After calculating and analyzing the polynomial function, non-polynomial function, and selecting different initial points for these two functions, research found that for simple polynomial functions, exponential functions, and even complex functions combined with the two Choosing any variable-scale matrix algorithm can quickly calculate the result, and it is basically not affected by the initial point selection. In the process of solving the “banana function” in the polynomial function, the DFP algorithm is optimal in terms of the number of iterations and the calculation time. Although the BFGS algorithm has better numerical stability, it is better for the “banana function” The calculation time is relatively long, and there are many iterations. When studying the logarithmic function, this article found that the performance of the “banana function” is not good, but the calculation performance of the BFGS(2) algorithm is the best. Finally, this article selected different initial points for the two functions and found that the numerical decline of the DFP algorithm is indeed unstable, while the BFGS algorithm is more stable than it, especially the BFGS(3) algorithm, which has the smallest change.