svd prescision is very bad.
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Kobi
el 13 de Oct. de 2014
Comentada: Andreas Goser
el 14 de Oct. de 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 comentarios
Roger Stafford
el 14 de Oct. de 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.
Respuesta aceptada
Andreas Goser
el 14 de Oct. de 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 comentarios
Oleg Komarov
el 14 de Oct. de 2014
Editada: Oleg Komarov
el 14 de Oct. de 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
Más respuestas (1)
Roger Stafford
el 14 de Oct. de 2014
Editada: Roger Stafford
el 14 de Oct. de 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.
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