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Step-asynchronous successive overrelaxation updates the values contained in a single vector using the usual Gauss-Seidel-like weighted rule, but arbitrarily mixing old and new values, the only constraint being temporal coherence: you cannot use a value before it has been computed. We show that given a nonnegative real matrix $A$, a $sigmageqrho(A)$ and a vector $boldsymbol w>0$ such that $Aboldsymbol wleqsigmaboldsymbol w$, every iteration of step-asynchronous successive overrelaxation for the problem $(sI- A)boldsymbol x=boldsymbol b$, with $s >sigma$, reduces geometrically the $boldsymbol w$-norm of the current error by a factor that we can compute explicitly. Then, we show that given a $sigma>rho(A)$ it is in principle always possible to compute such a $boldsymbol w$. This property makes it possible to estimate the supremum norm of the absolute error at each iteration without any additional hypothesis on $A$, even when $A$ is so large that computing the product $Aboldsymbol x$ is feasible, but estimating the supremum norm of $(sI-A)^{-1}$ is not.
We give improved algorithms for the $ell_{p}$-regression problem, $min_{x} |x|_{p}$ such that $A x=b,$ for all $p in (1,2) cup (2,infty).$ Our algorithms obtain a high accuracy solution in $tilde{O}_{p}(m^{frac{|p-2|}{2p + |p-2|}}) le tilde{O}_{p}(m^
We present faster high-accuracy algorithms for computing $ell_p$-norm minimizing flows. On a graph with $m$ edges, our algorithm can compute a $(1+1/text{poly}(m))$-approximate unweighted $ell_p$-norm minimizing flow with $pm^{1+frac{1}{p-1}+o(1)}$ o
Hyperparameter optimization (HPO) is increasingly used to automatically tune the predictive performance (e.g., accuracy) of machine learning models. However, in a plethora of real-world applications, accuracy is only one of the multiple -- often conf
The paper proposes a novel event-triggered control scheme for nonlinear systems based on the input-delay method. Specifically, the closed-loop system is associated with a pair of auxiliary input and output. The auxiliary output is defined as the deri
Although the operator (spectral) norm is one of the most widely used metrics for covariance estimation, comparatively little is known about the fluctuations of error in this norm. To be specific, let $hatSigma$ denote the sample covariance matrix of