And Foreign Several Algorithms Comparative Study

In this thesis, the algorithms of uncertain analysis, interpolation and numerical solution of high degree equation were selected to be studied among ancient china, India, Arabia, Japan and the west, in the way of historical analysis, mathematical analysis and comparison analysis etc.By reviewing the algorithms of uncertain analysis in ancient China, India and the West, this paper points out that the form that a problem was brought forward initially was the key factor to the shaping of the special algorithm. For a number, being divided by two numbers may cause indeterminate equations (in India) while by three numbers may cause group of congruence (in China). And then the conclusion can be obtained that the DAYANQIUYISHU (a algorithm of solution to congruence) and Kuttaka (a algorithm of indeterminate equations of the first degree) were mature algorithms; the algorithm in transcript of Getinggen was only a try.By reviewing the interpolation algorithm in ancient China (also in India and Arabia) and comparing this of Newton and Lagrange, it is obvious that orient algorithm had to be completed using the characteristics of the practical problem, so it was difficult to breakthrough generally. But the problem in the face of Newton and Lagrange was of universality so they succeeded in getting a general form.By reviewing the algorithm of numerical solution to high degree equation in ancient China and ancient Arabia and comparing this of Viete, Newton, Raphson and Horner, we can see that the ZENGCHENGKAIFANGFA (a algorithm of numerical solution to high degree equation) could obtain the solution digit by digit while the algorithm of Newton or Horner got the solution by digits. The latter would create the recurrence method that can also be applied to transcendental equation. Horner did draw on Budan's work of transformations of polynomial equation and then achieved to the same effect as the ZENGCHENGKAIFANGFA.The methodology of algorithm comparison study is discussed briefly.