# Monomial interpolation¶

Copyright (C) 2010-2020 Luke Olson

Copyright (C) 2020 Andreas Kloeckner

## MIT License

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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]:

<matplotlib.collections.LineCollection at 0x7f6d60f82c88>

- 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]:

686.43494181859546

In [ ]:

```
```