Monomial interpolation¶
In [1]:
import numpy as np
import numpy.linalg as la
import matplotlib.pyplot as pt
In [3]:
x = np.linspace(0, 1, 200)
Now plot the monomial basis on the interval [0,1] up to $x^9$.
In [4]:
n = 10
for i in range(n):
pt.plot(x, x**i)
pt.vlines(np.linspace(0, 1, n), 0, 1, alpha=0.5, linestyle="--")
Out[4]:
- How do the entries of the Vandermonde matrix relate to this plot?
- Guess the condition number of the Vandermonde matrix for $n=5,10,20$:
In [5]:
n = 5
V = np.array([np.linspace(0, 1, n)**i for i in range(n)]).T
la.cond(V)
Out[5]:
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