svd prescision is very bad.

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Kobi
Kobi on 13 Oct 2014
Commented: Andreas Goser on 14 Oct 2014
it appears to be that when i use SVD i loose prescision how can i avoid loosing prescision and use svd function?
[U,S,V]=svd(T);
T=U*S*V'
the first T Matrix and the second are not the same.
here a comparation of the matrix before svd and after:
>> T
T =
-0.4609 + 0.4970i 0.0023 + 0.0267i -0.0267 + 0.0028i
0.0023 + 0.0270i -0.5192 - 0.4982i -0.0023 - 0.0267i
-0.0267 + 0.0028i -0.0023 - 0.0270i -0.4609 + 0.4970i
>> [U,S,V]=svd(T); >> Tsvd=U*S*V'
Tsvd =
-0.4609 + 0.4970i 0.0023 + 0.0267i -0.0267 + 0.0028i
0.0023 + 0.0270i -0.5192 - 0.4982i -0.0023 - 0.0267i
-0.0267 + 0.0028i -0.0023 - 0.0270i -0.4609 + 0.4970i
>> difference=T-Tsvd
difference =
1.0e-15 *
-0.0555 - 0.1110i 0.0247 - 0.0312i -0.4025 + 0.3092i
-0.0278 - 0.0173i 0.0000 - 0.3331i -0.0494 + 0.0555i
-0.0486 + 0.0867i 0.0694 + 0.1076i 0.0000 + 0.0555i
  4 Comments
Roger Stafford
Roger Stafford on 14 Oct 2014
Kobi, that is just expected round-off error out at the fifteenth decimal place. You can't expect any better precision than that using double precision floating point numbers. After all, these numbers have only 53 bits in their significands. Your description of "very bad" is quite unfair.
Stephen23
Stephen23 on 14 Oct 2014
Edited: Stephen23 on 14 Oct 2014
Some information on Floating Point Numbers in MATLAB:

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Accepted Answer

Andreas Goser
Andreas Goser on 14 Oct 2014
Please let us know how familiar your are with numerical mathematics. The effect you see here is to be expected, but I do not want to come across as too blunt just pointing you to
eps
I could find a document that describes a bit about the why.
  3 Comments
Oleg Komarov
Oleg Komarov on 14 Oct 2014
Edited: Oleg Komarov on 14 Oct 2014
Where do you take 25 digits from?
>> fprintf('%.20f\n',pi)
3.14159265358979310000
>> fprintf('%.20f\n',eps(pi))
0.00000000000000044409
>> fprintf('%.20f\n',pi+eps(pi))
3.14159265358979360000
Andreas Goser
Andreas Goser on 14 Oct 2014
I can recommend this article for a deeper understanding.

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More Answers (1)

Roger Stafford
Roger Stafford on 14 Oct 2014
Edited: Roger Stafford on 14 Oct 2014
You cannot expect them to be exactly the same because of rounding errors. Have you compared them using "format long" to see how significant the differences are?
If you are still unsatisfied, please give a representative sample of what you have observed.
  1 Comment
Kobi
Kobi on 14 Oct 2014
example has been posted in the original question.

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