# ICE 8

As usual, we regret that this is a made-up example, but it is just a way to make a point, and to use the linalg subpackage of scipy. Incidentally, I tried to use the Klamath Flow data to make a real problem involving averaging, but it did not really illustrate the ideas adequately, and would have involved too many technical issues for an ICE.

Use the Scipy function `linalg.hilbert()` to make a
Hilbert matrix \(A\) of dimension 100. Make a solution vector \(x\)
composed of 100 ones, and find a right-hand-side vector \(y\)
as \(y=Ax.\)

- Now solve for \(x\) using the
`linalg.solve()`function. Compare with the actual solution \(x\). - Use Tikhonov regularization to solve for \(x\). Compare.
- Use a Truncated SVD to solve for \(x\). Compare.
- If time permits, do all this also for a uniformly distributed random vector for \(x\), and/or for a sinusoidal vector with 3-5 oscillations.

Assignment 1 is posted.