## svd prescision is very bad.

### Kobi (view profile)

on 13 Oct 2014
Latest activity Commented on by Andreas Goser

on 14 Oct 2014

### Andreas Goser (view profile)

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

Show 1 older comment
Kobi

### Kobi (view profile)

on 14 Oct 2014
example has been posted in the original question.
Roger Stafford

### Roger Stafford (view profile)

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.
Stephen Cobeldick

### Stephen Cobeldick (view profile)

on 14 Oct 2014
Some information on Floating Point Numbers in MATLAB:

### Andreas Goser (view profile)

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.

Kobi

### Kobi (view profile)

on 14 Oct 2014
i'm familiar with numerical mathematics pi is 3.14...... on double precision is 25 digits after the floating point also on e 2.71..... (natural number)
i tried to open the svd function to see what operation cause that
>> open svd
nothing there only comments. i don't think the error is because of the matrix product can you please point me to the math in svd that cause this error?
Oleg Komarov

### Oleg Komarov (view profile)

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

on 14 Oct 2014

### Roger Stafford (view profile)

on 14 Oct 2014
Edited by Roger Stafford

### Roger Stafford (view profile)

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.

Kobi

### Kobi (view profile)

on 14 Oct 2014
example has been posted in the original question.