Copyright (C) 2020 Andreas Kloeckner

In [1]:

```
import numpy as np
```

Here's an upper-triangular matrix $A$ and two vectors $x$ and $b$ so that $Ax=b$.

See if you can find $x$ by computation.

In [2]:

```
n = 5
A = np.random.randn(n, n) * np.tri(n).T
print(A)
x = np.random.randn(n)
print(x)
b = A @ x
```

In [3]:

```
xcomp = np.zeros(n)
for i in range(n-1, -1, -1):
tmp = b[i]
for j in range(n-1, i, -1):
tmp -= xcomp[j]*A[i,j]
xcomp[i] = tmp/A[i,i]
```

Now compare the computed $x$ against the reference solution.

In [4]:

```
print(x)
print(xcomp)
```

Questions/comments:

- Can this fail?
- What's the operation count?