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- W3037473623 abstract "Let $M=(m_{ij})$ be a symmetric matrix of order $n$ whose elements lie in an arbitrary field $mathbb{F}$, and let $G$ be the graph with vertex set ${1,ldots,n}$ such that distinct vertices $i$ and $j$ are adjacent if and only if $m_{ij} neq 0$. We introduce a dynamic programming algorithm that finds a diagonal matrix that is congruent to $M$. If $G$ is given with a tree decomposition $mathcal{T}$ of width $k$, then this can be done in time $O(k|mathcal{T}| + k^2 n)$, where $|mathcal{T}|$ denotes the number of nodes in $mathcal{T}$. Among other things, this allows one to compute the determinant, the rank and the inertia of a symmetric matrix in time $O(k|mathcal{T}| + k^2 n)$." @default.
- W3037473623 created "2020-07-02" @default.
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- W3037473623 date "2020-06-01" @default.
- W3037473623 modified "2023-09-27" @default.
- W3037473623 title "Efficient diagonalization of symmetric matrices associated with graphs of small treewidth" @default.
- W3037473623 doi "https://doi.org/10.4230/lipics.icalp.2020.52" @default.
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