Issue finding numerical error (problem with MATLAB's precision?)
3 views (last 30 days)
Show older comments
I'm trying to recreate some code that a TA showed me the other day. Suppose we have the system Ax=b. Let's say A = [2,1,1,0;4,3,3,1;8,7,9,5;6,7,9,8]. And let's say b = [1;1;-1;-3]. I saw a trick in MATLAB that can solve this equation using the "\" symbol. So A \ b should yield the following:
ans =
1.0000
0.0000
-1.0000
-0.0000
If you subtract this from the true solution:
(A \ b) - [1;0;-1;0]
ans =
1.0e-15 *
-0.2220
0.2538
0
-0.0912
Then you can actually see the error in MATLAB's solution versus the actual solution. My issue is that I cannot recreate this. When I do A \ b I get this:
ans =
1
0
-1
0
>> (A \ b) - [1;0;-1;0]
ans =
0
0
0
0
Therefore I cannot see the error, or this answer is just very imprecise-I'm not sure. How can I recreate the correct output? Is there another way I can see numerical error from an approximated solution versus the actual solution in MATLAB?
0 Comments
Answers (2)
Andrew Newell
on 16 Mar 2015
Edited: Andrew Newell
on 16 Mar 2015
That pesky MATLAB - getting more accurate all the time! Here is an example that I got from the blog article Floating Point Comparisons in Matlab:
x = 0.8-0.7;
x-0.1
On my computer, that returns 8.3267e-17 (which is still pretty good!).
2 Comments
Andrew Newell
on 17 Mar 2015
Edited: Andrew Newell
on 17 Mar 2015
Did you try this example from the same article?
K = 7;
s = zeros(K,1);
for k = 1:K
s(k) = sum((10^-k)*ones(10^k,1));
end
s
e = abs(s - 1)
Jan
on 17 Mar 2015
Edited: Jan
on 17 Mar 2015
Which format is active in the command window? What do you get with this:
format long g
(A \ b) - [1;0;-1;0]
Are A and B arrays of type double?
3 Comments
Andrew Newell
on 17 Mar 2015
I fixed that for you. You should be able to click on "Edit" and fix it yourself, though.
See Also
Categories
Find more on Get Started with MATLAB in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!