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## Feast RCI

Hello,

I have to solve the generalized eigen problem  Ax = λ Bx , where A is symmetric, positive-definite, and B is symmetric and not positive definite. I read that the FEAST algorithm can solve only the eigen system where B is positive definite. So I tried to solve the reverse problem, swapping A and B, and solving for 1/λ, but then the range of eigenvalues gets inverted, and I need to find the largest eigenvalues instead of the smallest. Unfortunately the matrix A is big and the algorithm takes too much time to find the eigenvalues and the eigenvectors, for the reverse problem! I understood that is possible to use the feast_rci to solve the direct problem where B can be not positive definite, am I correct? If yes where I can find a simple example  that uses PARDISO for factorization  and for the other operations required by the feast_rci? I've already read this page https://software.intel.com/en-us/node/521741#24EF00BB-984C-442C-889B-58B7C042C86C but if you can provide a simple example that uses PARDISO or other mkl function, it could be easier for me to understand how to solve my problem!

Giovanni.

7 Replies Employee
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Hi

sample codes of Feast and PARDISO can be found in the example folder of mkl (\$(MKLROOT)\examples\examples_core_c.zip\solvers_eec\source). Beginner
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Hi Jing,

Thanks for your reply, I studied the example code you suggested and I adapted it to my code, but due to the fact tha Feast RCI algorithm still depends on the interval emin-emax, if the upper bound (emax) is too far from the grater eigeinvalue in that interval, the value of this eigenvalue is very different from the expected one . Instead if a choose a narrower interval where the upper bound is very close to the last searched eigenvalue the result is correct! Is there a way to estimate the upper bound of the search interval?

Giovanni. Beginner
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Doing some more test, it seems that the FEAST RCI algorithm finds the greatest eigenvalues instead of the lowest one  for every interval passed. If the interval is narrower enough to contain only the searched eigenvalues, obviously the values returned are correct!

Do you have any suggestions? Moderator
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Giovanni, we have solution for such cases ( estimation # of EV into searching interval. this is what FEAST 3.0 has ) in the form of experimental package which you may try to evaluate.Just let us know. Beginner
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Thanks for your reply, I'm using Intel MKL Math library 11.3 and I think that includes only FEAST 2.1. If I am correct, where can I download the experimental package?

Giovanni. Moderator
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yes, it will work with version 11.3 ( the current is MKL 2017) of Intel MKL. Beginner
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Where can I find the documentation that describes the use of FEAST 3.0? Or Can you give me a small example that explains the estimation of eigenvalues in a search interval? 