正弦函數(shù)擬合計算

1、精品資料歡迎下載正弦函數(shù)擬合計算一、正弦函數(shù)的一般表達式的建立正弦函數(shù)的一般表達式為：yx0 sin( x1t x2 )x3（ 1）對于一系列的 n 個點 ( n3) ：(t i , yi), i 0,1, , n1（ 2）要用點 (ti , yi ), i 0,1,n1 擬合計算上述方程，則使：n12Sx0 sin( x1tix2 )x3yii0最小。要使得 S 最小，應(yīng)滿足：S0,k 0,1,2 ,3xkS2 x0sin( x1tix2 )x3yisin( x1ti x2 )x0S2 x0sin( x1tix2 )x3yix0ti cos(x1tix2 )x1即：S2 x0sin( x1t

2、ix2 )x3yix0 cos(x1tix2 )x2S2 x0sin(x1tix2 )x3yix3x00x0 s i nx(1tix2 )x3yis i nx(1tix2 )0x0 s i nx(1tix2 )x3yi.ti c o sx(t1 ix2 )0（ 3）x0 s i nx(1tix2 )x3yic o sx(t1ix2 )0x0 s i nx(1tix2 ) x3yi0解上述 4 元非線性方程組，即可得到正弦函數(shù)的一般表達式的系數(shù)：x0 , x1 , x2 , x3 。二、多元非線性方程組解法精品資料歡迎下載對于 n 元非線性方程組，記：F Xf0 ( X ), f1 ( X ),

3、 , f n 1 ( X ) T ， X x0 , x1 , , xn 1以及雅克比矩陣f0 ( X )f0 ( X )f0 ( X )f 0 ( X )x0x1x2x3f1 ( X )f1 (X )f1 ( X )f1 ( X )F'(X)f2x0x1x2x3( X )f 2 (X )f2 ( X )f 2 ( X )x0x1x2x3f3 ( X )f3 ( X )f3 ( X )f 3 ( X )x0x1x2x3即：f 0 ( X )f 0 ( X )f0 ( X )f0 (X )x0x1x2x3x0f 0 ( X )f1 ( X )f1( X )f1 ( X )f1 ( X )x

4、0x1x2x3x1f 1( X )f 2 ( X )f 2 ( X )f2 ( X )f2 ( X ) .x2f 2 ( X )（ 5）x0x1x2x3x3f 3 ( X )f 3 ( X )f3 ( X )f3 ( X )f3 ( X )x0x1x2x3三、正弦函數(shù)的一般表達式系數(shù)求解要擬合正弦函數(shù)的一般表達式（1）的系數(shù)，線性方程組（5）中的表達式為：精品資料歡迎下載f0 ( X )x0 sin( x1tix2 )x3yisin(x1tix2 )f1 ( X )x0 sin( x1tix2 )x3yiti cos(x1tix2 )f2 ( X )x0 sin(x1tix2 )x3yicos

5、(x1tix2 )f3 ( X )x0 sin( x1tix2 ) x3yif 0 ( X )sin 2 (x1t ix2 )x0f 0 ( X )x0ti sin 2( x1tix2 )( x3yi )ti cos(x1t i x2 )x1f 0 ( X )x0 sin 2( x1t ix2 )( x3yi ) cos( x1tix2 )x2f 0 ( X )sin( x1tix2 )x3f1 ( X )1ti sin 2( x1tix2 )x02f1 ( X )2cos2( x1tix2 )( x32sin( x1tix2 )x1x0tiyi )tif1 ( X )x0ti cos2( x

6、1ti x2 )( x3yi )ti sin(x1tix2 )x2f1 ( X )ti cos(x1tix2 )x3f 2 ( X )1sin 2( x1tix2 )x02f 2 ( X )x0ti cos2(x1tix2 )( x3yi )t i sin(x1tix2 )x1f 2 ( X )x0 cos2( x1t ix2 )( x3 yi ) sin(x1tix2 )x2f 2 ( X )cos(x1tix2 )x3f 3 ( X )sin(x1tix2 )x0f 3 ( X )x0t i cos( x1 tix2 )x1f 3 ( X )x0 cos(x1tix2 )x2f 3 ( X )nx3根據(jù)前面所述的Newton 迭代法，先給出x0 , x1 , x2 , x3 的初值 X 0 ，代入公式（5）求得：精品資料歡迎下載XkxxxxT0