[MATLAB数学相关] 急求教大侠们：曲线拟合，尽量光滑

[olivetianqin]

有这么h—mu这么一组数：

其中h=[-9000,-8000,-7000,-6000,-5000,-4000,-3000,-2000,-1100,-1000,-900,-800,-700,-600,-500,-400,-300,-250,-200,-160,-140,-120,-100,-90,-80,-70,-60,-46,-36,-30,-25,-20,-17,-15,-13,-11,-10,-9,-8,-7,-6.30000000000000,0,6.30000000000000,7,8,9,10,11,13,15,17,20,25,30,36,46,60,70,80,90,100,120,140,160,200,250,300,400,500,600,700,800,900,1000,1100,2000,3000,4000,5000,6000,7000,8000,9000];

mu=[5.00000000000000e-06,7.50000000000000e-06,1.00000000000000e-05,1.00000000000000e-05,1.50000000000000e-05,2.00000000000000e-05,2.50000000000000e-05,3.50000000000000e-05,6.25000000000000e-05,0.000100000000000000,0.000100000000000000,0.000100000000000000,0.000100000000000000,0.000100000000000000,0.000100000000000000,0.000150000000000000,0.000200000000000000,0.000300000000000000,0.000325000000000000,0.000375000000000000,0.000750000000000000,0.000750000000000000,0.000750000000000000,0.00100000000000000,0.00150000000000000,0.00250000000000000,0.00300000000000000,0.00541666700000000,0.00583333300000000,0.00933333300000000,0.0140000000000000,0.0230000000000000,0.0350000000000000,0.0475000000000000,0.0600000000000000,0.102500000000000,0.130000000000000,0.145000000000000,0.145000000000000,0.117142857000000,0.0809523810000000,0.0476190480000000,0.0809523810000000,0.117142857000000,0.145000000000000,0.145000000000000,0.130000000000000,0.102500000000000,0.0600000000000000,0.0475000000000000,0.0350000000000000,0.0230000000000000,0.0140000000000000,0.00933333300000000,0.00583333300000000,0.00541666700000000,0.00300000000000000,0.00250000000000000,0.00150000000000000,0.00100000000000000,0.000750000000000000,0.000750000000000000,0.000750000000000000,0.000375000000000000,0.000325000000000000,0.000300000000000000,0.000200000000000000,0.000150000000000000,0.000100000000000000,0.000100000000000000,0.000100000000000000,0.000100000000000000,0.000100000000000000,0.000100000000000000,6.25000000000000e-05,3.50000000000000e-05,2.50000000000000e-05,2.00000000000000e-05,1.50000000000000e-05,1.00000000000000e-05,1.00000000000000e-05,7.50000000000000e-06,5.00000000000000e-06];

其中以h为横轴，mu为纵轴，想要有具体的函数表达式可以拟合h--mu的尽量光滑的曲线（不要求每个点都相对，大致的走向轮廓一样就可以），因为用这个结果来进行的后续计算需要这条曲线是光滑的，请问大家该如何处理？

谢谢，~

[silas_xue]

lz 使用fit( )函数 具体选项和参数 可以参考matlab中的help

Thx for reading.
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[laosam280]

我采用三种不同的公式区拟合，得到的map-01的效果最好，另外两种的结果都在中心处有尖锐的波峰，效果不甚理想，从误差的图像也可以看出，中心处的值振荡很大。

[laosam280]

第三个公式的拟合结果误差柱状图。

[laosam280]

第三个公式的误差柱状图