svd prescision is very bad.

Question

Kobi 2014-10-13

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评论： Andreas Goser 2014-10-14

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

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Roger Stafford 2014-10-14

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 2014-10-14

编辑：Stephen23 2014-10-14

Some information on Floating Point Numbers in MATLAB:

http://www.mathworks.com/help/matlab/matlab_prog/floating-point-numbers.html

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Answer 1

Andreas Goser 2014-10-14

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/158501-svd-prescision-is-very-bad#answer_155054

在 MATLAB Online 中打开

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.

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Oleg Komarov 2014-10-14

编辑：Oleg Komarov 2014-10-14

在 MATLAB Online 中打开

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

Please, check: http://en.wikipedia.org/wiki/Double-precision_floating-point_format

Andreas Goser 2014-10-14

I can recommend this article for a deeper understanding.

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Answer 2

Roger Stafford 2014-10-14

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/158501-svd-prescision-is-very-bad#answer_155039

编辑：Roger Stafford 2014-10-14

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.