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Sparse dense matrix versus non-sparse dense matrix in eigenvalue computation

I have a matrix in the form of $2n\times 2n$ block matrix $$ A = \begin{pmatrix}O& W\\ J& D\end{pmatrix} $$ where, $O$ is an $n\times n$ zero-matrix; $W$ is a n-by-n diagonal matrix, $W = ...
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