In this paper, we develop a simple and novel method for determining sharp upper bounds on errors in approximate zeros of a given polynomial using Rouche's theorem from complex analysis. We compute the error bounds using non-linear optimization. Our bounds are scalable in the sense that we ...
Unique Capabilities and Industry Applications Quantum computing can solve “intractable problems”—complex issues that classical computers struggle to address—unlocking new solutions in several key industries. In traditional computing, approximations often create a margin of error of 5–20%. Quantum ...
reliance onInteger Linear Programming(ILP) solvers,SCAalgorithms, and various ML models hints at floating-point being used[49,84,89,91,133]. When these solvers’ convergence criteria permit such, one may consider switching to fixed-point formats within them before evaluating further approximations. ...
The motivation for this post is to try to improve upon past analyses of Dreidel, which involve various limitations, simplifying assumptions, and/or approximations in their solution; and to present exact probabilities and expected values for the game, that raise an interesting conjecture that appears...
averaged over qubit states distributed uniformly on the Bloch sphere,\(\overline{ {\mathcal E} }\). The inset shows the difference Δℰbetween the numerically calculated errors and their analytical first-order approximations (Table1), withdashed linesindicating the difference in maximum errors...
The Battacharia’s distance deals with Gaussianapproximations: • On the cumulated distributionsC, one can compute the Kolmogorov–SmirnovDKSor Cramer–Von MisesDCvMdistance: (3.37)DKS(q,i)=maxj(Cq(j)−Ci(j))andDCvM(q,i)=∑j(Cq(j)−Ci(j))2 ...
The goal is not only to design approximation algorithms, but also to analyze how approximations introduce errors and how these, in turn, affect the algorithm’s performance and power savings. The student will look at two classes of algorithms for imaging tasks, such as classification, ...
We present As-Is, an Anytime Speculative Interruptible System that takes an approximate program and executes it with time-proportional approximations. That is, an approximate version of the program output is generated early and is gradually refined over time, thus providing the run-time guarantee ...
“problems”, and “errors”). Some of these are duplicates or unrelated to Materials Project, and the vast majority of these are minor and don’t affect any results. Still, trying to exterminate the Materials Project’s bugs can be somewhat maddening – the past few years have demonstrated...
Computing on unreliable hardware means introducing approximations at the circuit level by using unintentionally faulty circuits or purpose-designed ones. Putting faulty chips that produce acceptable errors to use can increase production yield [22], while purpose-designed ones may bring significant savings ...