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laoyou
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GUEST, unregistred user!
我不大清楚后面的那两种光滑样条是如何拟合出来的，以及那个光滑因子的含义，如何定义
，或者如何从误差中取得，加上光滑因子的样条曲线方程是个什么样子，我最想弄懂第三种
Automatically smoothed spline 是如何得
来的，请yysun 老师或者哪位高人赐教！
我后来验证到第一种插值样条曲线是边界条件为自然拟合（边界点的二次导数为零）
的三次样条拟合，光滑因子为零就是指第一种插值样条拟合，我就是想知道光滑因子
不为零的表达式是什么样子的，
Spline methods
Spline is a piecewise third order polynomial which has knots at every standard concentration. The whole function and its first and second derivatives are
continuous. The general formula is：
Y( X) = a 0j +a 1j * X +a 2j * X ^2 +a 3j * X^3
where constants a ij are valid between standard j and standard (j+ 1).
There are three kinds of spline fitting methods:
1. Interpolation spline
which goes exactly through all standard responses. Often it oscillates because
standard points have random errors and there is no well behaved continuous function which passes through all the points. Therefore it is not recommended
for general use.
2. Presettable smoothed spline where the normalised smoothing parameter (S)
with a value between 0 and 1 must be given. 0 means interpolation and 1
smoothing within calculated errors (on the average).Normalisation makes the
factor independent of the number of standard points( n). The unnormalised
factor is nS.
3. Automatically smoothed spline which selects the degree of smoothing so that
it is the optimum which allows a function with no minima and maxima and a
maximum of one turning point. If the data are scattered very much the smoothing
is aborted after the following 8 steps:
Iteration
1 Fit using S = 0
2 Fit using S = 1/ 4
3 Fit using S = 1/ 2
4 Fit using S = 1
5 - 8 Fit after errors are multiplied by 1. 41
(SQR( 2)) near bad points (minima, maxima and turning points) using S = 1.
After every step the shape of the curve is checked and if there are no extremes
and max.1 turning point the curve is considered to be the optimum. The model of the curve is not checked because the selectable co- ordinate system makes it
impossible to know the shape.
，或者如何从误差中取得，加上光滑因子的样条曲线方程是个什么样子，我最想弄懂第三种
Automatically smoothed spline 是如何得
来的，请yysun 老师或者哪位高人赐教！
我后来验证到第一种插值样条曲线是边界条件为自然拟合（边界点的二次导数为零）
的三次样条拟合，光滑因子为零就是指第一种插值样条拟合，我就是想知道光滑因子
不为零的表达式是什么样子的，
Spline methods
Spline is a piecewise third order polynomial which has knots at every standard concentration. The whole function and its first and second derivatives are
continuous. The general formula is：
Y( X) = a 0j +a 1j * X +a 2j * X ^2 +a 3j * X^3
where constants a ij are valid between standard j and standard (j+ 1).
There are three kinds of spline fitting methods:
1. Interpolation spline
which goes exactly through all standard responses. Often it oscillates because
standard points have random errors and there is no well behaved continuous function which passes through all the points. Therefore it is not recommended
for general use.
2. Presettable smoothed spline where the normalised smoothing parameter (S)
with a value between 0 and 1 must be given. 0 means interpolation and 1
smoothing within calculated errors (on the average).Normalisation makes the
factor independent of the number of standard points( n). The unnormalised
factor is nS.
3. Automatically smoothed spline which selects the degree of smoothing so that
it is the optimum which allows a function with no minima and maxima and a
maximum of one turning point. If the data are scattered very much the smoothing
is aborted after the following 8 steps:
Iteration
1 Fit using S = 0
2 Fit using S = 1/ 4
3 Fit using S = 1/ 2
4 Fit using S = 1
5 - 8 Fit after errors are multiplied by 1. 41
(SQR( 2)) near bad points (minima, maxima and turning points) using S = 1.
After every step the shape of the curve is checked and if there are no extremes
and max.1 turning point the curve is considered to be the optimum. The model of the curve is not checked because the selectable co- ordinate system makes it
impossible to know the shape.