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I have a matrix K in Petsc. I want to delete the $n^{th}$ row and $n^{th}$ column of this matrix and restructure it. I am a beginner in Petsc. Can you suggest how to do it?

Example: I have matrix K of size 100 x 100. I want to remove the 10th row and 10th column so that the remaining restructured matrix is 99 x 99.

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You don't do that for large and sparse matrices. It's an inefficient operation. Rather, you zero out the $n$th row and column and put a nonzero entry on the diagonal. Then you think about what operations that you wanted to do on the $99\times 99$ matrix need to look like on the modified $100\times 100$ matrix.

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  • $\begingroup$ Thank you for your reply Sir! I want to compute the smallest magnitude eigenvalues a tangent stiffness matrix (FEM). Assuming I am not concerned with the efficiency, as it is one time calculation, would you suggest a way to restructure the matrix? I agree with your "operations" analogy on modified matrix, in that that case, willI I have unit corresponding eigen values? $\endgroup$ – ARUN KUMAR Jun 3 '20 at 5:24
  • $\begingroup$ Yes, if you delete a row and column and place a value of $a$ on the diagonal, you get one eigenvalue equal to $a$. In other words, if you are looking for the smallest eigenvalue, you want to choose $a$ to equal, for example, the magnitude of the largest diagonal entry in hopes that $a$ is then larger than the smallest eigenvalue. You generally want to ensure that $a$ is on the same order of magnitude as the other entries in the matrix to make sure the resulting matrix remains well-conditioned. $\endgroup$ – Wolfgang Bangerth Jun 3 '20 at 16:33
  • $\begingroup$ I do think that zeroing out rows and columns is much easier to implement than actually shrinking the size of the matrix to $99\times 99$. $\endgroup$ – Wolfgang Bangerth Jun 3 '20 at 16:34
  • $\begingroup$ Got it! Thanks Sir! $\endgroup$ – ARUN KUMAR Jun 4 '20 at 16:17

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