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Approximating the inverse of a diagonally dominant matrix with positive elements

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abstract

For an $n\times n$ diagonally dominant matrix $T=(t_{i,j})_{n\times n}$ with positive elements satisfying certain bounding conditions, we propose to use a diagonal matrix $S=(s_{i,j})_{n\times n}$ to approximate the inverse of $T$, where $s_{i,j}=\delta_{i,j}/t_{i,i}$ and $\delta_{i,j}$ is the Kronecker delta function. We derive an explicitly upper bound on the approximation error, which is in the magnitude of $O(n^{-2})$. It shows that $S$ is a very good approximation to $T^{-1}$.

fields

econ.EM 1

years

2024 1

verdicts

UNVERDICTED 1

representative citing papers

Bagging the Network

econ.EM · 2024-10-31 · unverdicted · novelty 7.0

A bagging-based estimator for dyadic networks with fixed effects attains asymptotic normality and the Cramér-Rao bound for both TU and NTU links by using joint MOM, Le Cam refinement, and split-network jackknife.

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  • Bagging the Network econ.EM · 2024-10-31 · unverdicted · none · ref 64 · internal anchor

    A bagging-based estimator for dyadic networks with fixed effects attains asymptotic normality and the Cramér-Rao bound for both TU and NTU links by using joint MOM, Le Cam refinement, and split-network jackknife.