Topic: 请教数学问题。 @佛州华人论坛:佛州枫下论坛 The Rolia Forum of Florida

是要做回归分析（Regression Analysis）吗？ -urmylove(麻袋); 2010-1-26 (#5838915@0)
1. Yes, 2. Yes, 3. Yes or no, any function can be written in the sum of many sine/cosine functions (Fourier Transform), but not all the summation can be written in this concise form. 4. Not sure, but you can try "approximation". -wireless_mouse(无线小滑鼠); 2010-1-26 (#5838947@0)
续 -urmylove(麻袋); 2010-1-26 {801} (#5838949@0)

Thank you thank you thank you. -registereduser(立牌坊); 2010-1-28 {693} (#5844038@0)

每组的点数是一样的。多项式以确定，但最高次没有确定，但会有个范围，比如最高不超过7。不是非要落在线上，但应该尽量接近线。 -registereduser(立牌坊); 2010-1-29 (#5846479@0)

先谢谢两位大侠。我要慢慢消化。 -registereduser(立牌坊); 2010-1-26 (#5839428@0)
标准答案问题1&2：N阶的polynomial 可以通过平面上N+1个点。
问题3&4：BSpline或者其通用型NURB是目前最好的算法。 -yxes(yob); 2010-1-26 {100} (#5839810@0)

刚看明白Polynomial的概念。也看了Cubic B-spline，Cubic Hermite和NURB的概念。我把我的问题进一步提炼，看大侠能不能给我直接答案,或告诉我哪种B-spline可满足我的要求：1，我的数组可以在X轴上简化为连续的值，这样数组就可以变为单一Dimension的数组。我想这样会简单很多。
2，我希望表达式一定要Polynomial，而且一定要aX^5+bX^4+cX^3+dX^2+dX+e=0这个式样。算法中Term的数量最好能由User控制。

谢谢大侠。 -registereduser(立牌坊); 2010-1-28 {226} (#5844749@0)

那就按照你希望的来，这样简单。已知 (X1,Y1), (X2,Y2)...(XN,YN), 依次带入polynomial,得到一N阶线性方程组，求解，结果就是系数。 -yxes(yob); 2010-1-28 {93} (#5845754@0)

Algorithm : Gaussian elimination. Acurracy ? the curve can exaxtly path all your points.This solution is cheap, downside is curve vibrate dramatically with some point set. -yxes(yob); 2010-1-29 {83} (#5847485@0)

Thanks. Gaussian elimination however is too costly.What I want indeed is a balance point where both cost and accuracy are acceptable. Since groups of sets might be very dramatic, I therefore need to develop an algorithm to determine the number of terms in polynomial (the cost) based on the situation of each group.

Thus, I will stick on the B-spline. Of course, before that, I need to pick the best suitable B-spline. -registereduser(立牌坊); 2010-1-29 {371} (#5847790@0)

这个得具体问题具体分析。Regression有很多方法，没有哪个是绝对好的。你现在的问题是两个变量，比较容易。如果是许多变量，问题会复杂的多。 -ding_ding(丁_丁); 2010-1-27 (#5840507@0)

@Florida