gibson:teaching:fall-2014:iam961:hw5
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gibson:teaching:fall-2014:iam961:hw5 [2014/12/08 11:02] gibson |
gibson:teaching:fall-2014:iam961:hw5 [2014/12/14 05:08] (current) gibson |
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| 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')''. |
| 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. | 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. | ||
gibson/teaching/fall-2014/iam961/hw5.1418065320.txt.gz · Last modified: 2014/12/08 11:02 by gibson
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