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For questions about factorization, the decomposition of mathematical objects (e.g. natural numbers, polynomials) into products of smaller objects (e.g. primes, lower degree polynomials).

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How to do LU factorization efficiently based on the factorized result added with a low-rank ...

Is there any efficient way to compute the LU factorization of $A^{\text{new}}$? … Normally, a full re-factorization of $A^{\text{new}}$ is $O(n^3)$ complexity, and I am seeking a possible $O(n^2)$ algorithm with the reuse of $L^{\text{old}}$ and $U^{\text{old}}$ that have been previously …
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