gibson:teaching:fall-2014:iam961:hw5
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
gibson:teaching:fall-2014:iam961:hw5 [2014/12/08 10:48] gibson |
gibson:teaching:fall-2014:iam961:hw5 [2014/12/14 05:08] (current) gibson |
||
|---|---|---|---|
| Line 28: | Line 28: | ||
| 2. Let $x$ be a random M vector with normally-distributed components. Let $b = A x$. | 2. Let $x$ be a random M vector with normally-distributed components. Let $b = A x$. | ||
| - | 3. Do the GMRES iteration and plot the normalized residual $\| A x_n - b\|/\|b\|$ and the normalized $x$ error $\| x_n - x \|$ as a function of the iteration number $n$. Plot the residual with circles and the error with dots, put them on the same plot, and use a logarithmic axis. | + | 3. Do the GMRES iteration and plot the normalized residual $\| A x_n - b\|/\|b\|$ and the normalized $x$ error $\| x_n - x \|$ as a function of the iteration number $n$. Plot the residual with circles and the error with dots, put them on the same plot, and **use a logarithmic axis for the errors**: e.g. ''semilogy(n,error,'b.',n,residual,'ro')''. |
| - | Set $M$ to a fairly small number, like 20 or 30 and produce three residual-and-error plots, for $\kappa=100$, $\kappa=10^6$, $\kappa=10^16$ | + | For testing and developing your code, set $M$ to a small number like 10 and $\kappa$ to $10^8$. Your GMRES code should go all the way to $n=M$ iterations. Your code should have a for-loop to handle iterations $n=1$ to $M-1$ followed by some special-case code to handle the last $n=M$th iterate --the last iteration works a little differently. |
| + | |||
| + | Once your code is working (the residual is $10^{-16}$ at the last iterate), set $M$ to a moderately small number like 30 and produce four residual-and-error plots, for $\kappa=100$, $\kappa=10^8$, $\kappa=10^{16}$, and $\kappa=10^{32}$. | ||
| + | |||
| + | Discuss your results. Is anything surprising? What can you explain about the behavior of the plots, given what you know about GMRES and $Ax=b$ problems in general? | ||
gibson/teaching/fall-2014/iam961/hw5.1418064493.txt.gz · Last modified: 2014/12/08 10:48 by gibson
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 3.0 Unported
