5 ms·
If you try to solve a linear system with a condition number of 3.73e16, it's not really correct to say that the problem lies with floating-point errors, because
by conistonwater 9y ago
If you try to solve a linear system with a condition number of 3.73e16, it's not really correct to say that the problem lies with floating-point errors, because the real problem is that you tried to solve an extremely ill-conditioned problem. The wrong answer you get is backward stable, in fact—it is the exact solution of a nearby perturbed system. One way to think of it is that the phrase "the answer you should get" is somewhat ambiguous. I don't think your example goes against the post's main points.
- Natsu 9y ago> the real problem is that you tried to solve an extremely ill-conditioned problem This makes it sound like you're saying just not to solve problems when they're too annoying, but I somehow don't think that's what you're trying to say.
- conistonwater 9y agoIn a way that's technically true, because solving ill-conditioned problems with noisy data is both difficult and the results are often meaningless. But you almost always have some choice about which of a multitude of subproblems you try and solve to reach your actual goal. It's like the difference between executing an algorithm and designing an algorithm. So instead of solving ill-conditioned subproblems, you spend your effort getting to well-conditioned subproblems instead. I think a common example of an ill-conditioned problem that's too annoying to solve is weather prediction past 2 weeks in advance, because it's a chaotic system, so I don't think what you're saying is wrong.
- deleted 9y ago[deleted]