11 questions linked to/from full rank update to cholesky decomposition
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### Can diagonal plus fixed symmetric linear systems be solved in quadratic time after precomputation?

Is there an $O(n^3+n^2 k)$ method to solve $k$ linear systems of the form $(D_i + A) x_i = b_i$ where $A$ is a fixed SPD matrix and $D_i$ are positive diagonal matrices? For example, if each $D_i$ is ...
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### Diagonal update of a symmetric positive definite matrix

$A$ is a $n \times n$ symmetric positive definite (SPD) sparse matrix. $G$ is a sparse diagonal matrix. $n$ is large ($n$ >10000) and the number of nonzeros in the $G$ is usually 100 ~ 1000. $A$ has ...
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### full rank update to cholesky decomposition for multivariate normal distribution

This question is a specialization of full rank update to cholesky decomposition, to which I hope to get a more positive answer. When calculating the minus log of the multivariate normal distribution, ...
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### Efficient approach for solving matrix plus diagonal matrix system that varies in time

When solving a system of ODEs, as part of a preconditioner, I get the system $(A + D(t))x = b(t)$ where $A$ is a sparse matrix and $D(t)$ is diagonal. I'm currently solving this by taking the LU-...
I am looking for a computationally cheap way to compute $x$ such that $$(L L^T + \mu^2 I)x = y$$ where $L \in \mathbb{R}^{n \times n}$ is a lower triangular definite positive matrix (with some very ...