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question about the complexity to calculate just one eigenvalue

Ye_C_1
Beginner
‎08-14-2016 09:05 PM
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As we know that the complexity of diagonalization of a matrix should be N^3, where N is the dimension of the matrix. 

In MKL, there are a lot of functions that can calculate just some of the eigenvalues.

I want to know that when we just calculate one eigenvalue, if the time cost is divided by N?

 

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Konstantin_A_Intel
Employee
‎08-16-2016 09:47 AM
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Hi Ye,

You cannot expect that the computation time will be N times lower for only one eigenvalue. Of course, some performance benefit can be expected, but you need to know that there're parts common for any number of eigenvalues (like reducing the matrix to triangular form) and which we cannot make faster.

Regards,

Konstantin

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