建部贤弘的累遍增约术与Romberg算法

TAKEBE'S REPEATED SHOYAKUJUTSU METHODAND ROMBERG ALGORITHM

日本和算家建部贤弘（１６６４－１７３９）为求圆周率创造了累遍增约术的数值逼近算法，这一算法长期以来没有引起和算史研究者的重视。这篇论文通过对这一算法的深入分析，首次指明它就是数值逼近中的Ｒｏｍｂｅｒｇ算法，而Ｒｏｍｂｅｒｇ算法发表于１９５５年，因而认为建部贤弘是Ｒｏｍｂｅｒｇ算法的初创者。并进一步分析了建部贤弘算法思想的中算源流。

Japanese mathematician Takebe ( 1664- 1739 ) created the Repeated Shoyaku- jutsu Method which is a kind of the numerical approaehing method , which has long been ig- nored by Japanese mathematics historians . In the paper , the author makes a thorough analysis of this method , and suggests that , it is just the Romberg Algorithm that is the numerical ap- proaehing method. The Romberg Method was published in 1955 ,so Takete's method is earlier than that of Romberg by 240 year. Finally , furthur analyses of Chinese source in Tabebu method are also made.