The interpolation is a method to estimate a value of a function fix) from its discrete values (for example, f(0), f(1),etc.). For this purpose, differences (for example, "first order difference" △1= f(1)-f(0) etc.) are used.rn The origin of the second order interpolation established at the time of Sui dynasty was the first order interpolation applied to the first differences. At the time of Tang dynasty, Yixing started to use the third difference, but his method was not third order interpolation.Yixing appfied the first order interpolation to thesecond differences (in other words, applied the second order interpolation to the first diferences), and the accuracyof the result was not so different from the previous second order interpolation.Yixing's method was a naturaldevelopmem of the method of Sui period.rn More than ten years ago,I published two papers regarding Chinese interpolation (bhashi (1994) and (1995).)At that time, some young Chinese researchers were also studying Chinese mathematical astronomy including the interpolation (Qu, Ji and Wang (1994)).Among them, Qu Anjing recently published a detailed monograph on Chinese mathematical astronomy (Qu (2005)). Qu's interpretation of Yixing's interpolation using the thirddifference is quite different from my interpretation.I would like to discuss this point in this paper.
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