About Schur complement

[libuxiao]

Recently,I am trying to solve a problem in the form of D-C*INVERS(A)*B, and A,B,C,D are all full matrix.I used to solve it by constructing a matrix and then called mumps to return a schur complement of it.But the memory use is imblanced.So now I want to use SCALAPACK to solve it.I am new to it and want to know whether there is any routine that can return the Schur complement of a matrix as mumps do.Or will I have to try to solve this problem by computing the inverse of matrix A,then multiply C and B?Is there any better advice?

[Julien Langou]

There is no Schur complement routine in ScaLAPACK but there is all the tools to write one. To perform

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D - C * inv(A) * B


with ScaLAPACK, you want to rewrite this as:

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D - C * ( A \ B )


where \ is the Matlab command that means 'solve AX = B'. (This is not done through X = inv(A) * B, this is done by a faster and more stable way.) \ is in ScaLAPACK, this is PxGESV. Then you just need to perform a matrix mulyiply, you can use PxGEMM.

Julien.

[libuxiao]

Thank you for your reply.It helps me a lot,thank you.