Solving Linear Systems in $\widetilde{O}(mn \log \fracκε)$ Bit Operations

We give a deterministic algorithm that solves a nonsingular linear system $Ax=b$, where $A\in\mathbb{R}^{n\times n}$ has $m$ nonzero entries and condition number $κ$, to any relative residual tolerance $0<ε\le1/2$ using $\widetilde{O(}mn\log(κ/ε))$ bit operations for inputs with logarithmically many