切比雪夫多项式拟合

切比雪夫多项式拟合，个人理解就是用其可以来拟合一个函数，如下面例子中x为1,2,3,4时，对应的y为1,3,5,4，我们用契比雪夫多项式拟合来表示这样的一个函数。

 例子：

import numpy.polynomial.chebyshev as chebyshev
import numpy as np
import numpy.linalg as linalg


x = np.array([1, 2, 3, 4])
y = np.array([1, 3, 5, 4])


deg = len(x) - 1
A = chebyshev.chebvander(x, deg)


print(A, "# A")
c = linalg.solve(A, y)
print(c,"# c")
for v in x:
        print( v, np.polynomial.Chebyshev(c)(v),"#p(%d)" % v)

结果：

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例子2：

根据输入x，拟合函数 cos(x)

import numpy.polynomial.chebyshev as chebyshev
import numpy as np
import numpy.linalg as linalg

x = np.linspace(0,1,10)
y = np.cos(x)



deg = len(x) - 1
A = chebyshev.chebvander(x, deg)


print(A, "# A")
c = linalg.solve(A, y)
print(c,"# c")
print("x值	", "拟合的y值	", "实际的y值	")
for v in x:
        print( v, np.polynomial.Chebyshev(c)(v), np.cos(v))

结果：

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参考：

http://liao.cpython.org/scipy09/