- 作者: 張高次; 謝聰智
- 作者服務機構: 中央研究院數學研究所
- 中文摘要: 為著要描述收集資料的各種性質,人們常根據已有的資料點找出適當的近似函數來探討它的性質。尋求這種近似函數的方法已有許多,最常用的例如最小方差法(LeastSquares),有理逼近法(Rational Approximation)或 Tchebycheff 逼近法等。 這裏我們想從另一個角度來討論這個問題。由於每種函數都有它所能滿足的微分方程式,最佳近似微分方程式的計算法可以說比近似函數的求法有更廣泛的含意。 Michael H. Reid 和 R. Stuart Mackay* 在討論系統識別(System Identifi-cation)問題時曾介紹一種利用線性規劃(Linear Programming)的方法找尋最佳近似微分方程式。由於他們所利用的 Simplex 程式對於探討結果的誤差估計所需要的反矩陣的資料無法求得,本文乃利用 Revised Simplex 的方法重新寫出 RSIMP 程式。在這個程式中,我們不但可以得到有關反矩陣的資料,並且在對於大系統問題之處理時對應之程式大大地減少了所需記憶空間。
- 英文摘要: For describing the collected data people try to find a suitable function to fitthe data. There are many methods to find the approximate function. The mostoften used ones are least square method, rational approximation and Tchebycheffapproach. In this paper we discuss the approximate problem from the other point ofview. Since in practise every function satisfies a differential equation the optimalapproximate differential equation approach is the most meaning than approximatefunction approach. Michael H. Reid and R. Stuart Machay have introduce linear programningmethod to find the optimal aproximate differential equation for system identifica-tion. The simplex used by them failed to give the inverse matrix, which is im-portant to measure error of result. By improved revised simple we rewrite RSIMP program by which the inversematrix was obtained. Furthrmore the program reduces the memory space for identi-fication of large scale system.
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