戴煦、项名达、夏鸾翔对迭代法的研究

DAI XU, XIANG MINGDA AND XIA LUANXIANG'S STUDIES ON THE ITERATIVE METHOD

本文通过对宋元以前的开方术及清代数学家戴煦等人的开方法和解数字方程法的分析研究,探讨了他们在迭代法方面的研究工作。笔者认为戴煦在中算史上首先使用了迭代法;项名达和夏鸾翔沿着这个方向继续深入研究,并取得了一些成果。他们在不了解外国工作的情况下,给出了几种开方和解数字方程的迭代程序,独立地得到了解数字方程的牛顿一拉弗森迭代法。这是19世纪中算史上的重要成果。

This paper deals with the iterative method of Chinese mathematicians by studying their methods of approximating the roots of numerical equations. It shows that Dai Xu (1805—1860) was the first Chinese mathematician who used the iterative method for extracting the square root of a number. Xiang Mingda (1789—1850) and his student Xia Luanxiang (1825—1864) were also interested in it. They developed the method by giving several iterative processes and obtained the same results as the Newton-Raphson method. The contribution of Dai, Xiang and Xia to the iterative method are important in the history of Chinese mathematics.