Efficient LU decomposition of matrix after updating diagonal

Asked Jun 02 '21 at 18:29

Active Jun 02 '21 at 18:29

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I am computing LU decomposition of $(kD + A)$ where $D$ is diagonal matrix with {$d_{1}$, $d_{2}$, ... , $d_{n}$}, $A$ is a real symmetric positive-definite matrix, $k$ is a number that changes on each iteration. D and A are always constant.

Now, my question is if there is an efficient way to compute the LU decomposition that does not involve computing the LU decomposition of a full matrix $(kD + A)$? For example calculate the LU decomposition only for $A$ and then update it depending on $kD$

asked Jun 02 '21 at 18:29

dimaMS

Do we have $d_1,\dots,d_n\geq 0$? If so, then you should probably be using a Cholesky decomposition rather than an $LU$ decomposition. – Ben Grossmann Jun 02 '21 at 18:36
yes, $d_{1}$,…,$d_{n}$$≥0$ – dimaMS Jun 02 '21 at 18:48

Efficient LU decomposition of matrix after updating diagonal

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