hi please go through the following article 

http://147.228.63.6/research/night_road/westminster.pdf

https://books.google.co.in/books?hl=en&lr=&id=vzQH3qA_RKkC&oi=fnd&pg=PR11&dq=papaers+on+advantage+and+disadvantages+of+linear+color+models+conversions&ots=DB2gn-q0R9&sig=i4JpobUAK_bLtEbNSuBREdsorlQ#v=onepage&q&f=false

Thanks Chethankumer for your answer. 

A couple thoughts:

1) Linear transforms are usually much faster to compute than non-linear transforms.

2) It's easier to chain together multiple linear transforms into a single linear transform.

3) It's often easier to see how the input color channels affect the output values when you have a linear matrix.

4) Partial derivatives are simple for linear transforms. Derivatives are used in understanding sensitivity, error propagation, and some forms of optimization. (CIECAM02 is an example of using optimization to improve a color transform.)

5) Metamers are easier to find.

The color space conversion has high-precision

Thanks Nick Loomis for your answer, seems great begin to find my answers.

 if you please provide me by more details or references 

Thanks Alessandro Artusi, I like your answer , and I have to prove the performance 

Poorvi H Patel,  Thanks for your answer, but , I couldn't understand what do you mean !!