# Question:How to compute inverse of a matrix for solving eigenvalue problem using Parallel programming?

## Question:How to compute inverse of a matrix for solving eigenvalue problem using Parallel programming?

Maple

I have a eigenvalue problem like:

[FF1]* {w}=N^2 *[FF2] *{w}

[FF1] and [FF2] are a*b matrices (non square matrix) , {w} are vectors(eigenvectors) and the values of N are eigenvalues.

I want to obtain eigenvalues and eigenvectors by computing Moore-Penrose pseudo-inverse of [FF2] and do the procedures below :

[FF2]^-1 * [FF1] *{w} =N^2 *{w}            ,        (assume  [FF2]^-1   is Moore-Penrose pseudo-inverse of [FF2]   )

[FF2]^-1 * [FF1] = [FF3]  ,  ( [FF3] is a b*b matrix- squre matrix)

so  [FF3] *{w}=N^2 *{w}

then I can use LinearAlgebra[Eigenvectors](FF3) to get eigenvalues and eigenvectors.

I know that Moore-Penrose pseudo-inverse of [FF2] * [FF1] isn't equal to Identity matrix. [FF2]^-1 * [FF1] <> [ I ] . But assume it can be. ( I have a solution for this problem) .

My biggest problem is [FF2] and [FF1] are large-scale sparse matrix and it takes hours or several days that maple can compute Moore-Penrose pseudo-inverse of [FF2]  and also LinearAlgebra[Eigenvectors](FF3).

Main question : can I compute Moore-Penrose pseudo-inverse and LinearAlgebra[Eigenvectors]  by using Parallel Programming?  if the answer is yes , how? give me an example please.

if the answer is No , is there any way (any algorithm) to find the inverse of a large non-sqaure matrix or eigenvalues of a large matrix faster?

please introduce some books for parallel programming in maple or general.

Thanks.

1.mw

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