Related papers: Mechanizing Olver's Error Arithmetic
In this work, we deal with an iteration method for approximating a fixed point of a contraction mapping using the Mann's algorithm under functional random errors. We first show its almost complete convergence to the fixed point by mean of…
We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…
Real-world applications of machine learning models are often subject to legal or policy-based regulations. Some of these regulations require ensuring the validity of the model, i.e., the approximation error being smaller than a threshold. A…
In this paper, we use reduced precision checking (RPC) to detect errors in floating point arithmetic. Prior work explored RPC for addition and multiplication. In this work, we extend RPC to a complete floating point unit (FPU), including…
To increase the ubiquity of machine learning it needs to be automated. Automation is cost-effective as it allows experts to spend less time tuning the approach, which leads to shorter development times. However, while this automation…
Rotation estimation plays a fundamental role in computer vision and robot tasks, and extremely robust rotation estimation is significantly useful for safety-critical applications. Typically, estimating a rotation is considered a non-linear…
Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing…
This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which…
In this work, the problem of 4 degree-of-freedom (3D position and heading) robot-to-robot relative frame transformation estimation using onboard odometry and inter-robot distance measurements is studied. Firstly, we present a theoretical…
The error on a real quantity Y due to the graduation of the measuring instrument may be represented, when the graduation is regular and fines down, by a Dirichlet form on R whose square field operator do not depend on the probability law of…
A machine learning model is calibrated if its predicted probability for an outcome matches the observed frequency for that outcome conditional on the model prediction. This property has become increasingly important as the impact of machine…
In this paper, we propose a novel method for estimating an elliptic shape approximation of a moving extended object that gives rise to multiple scattered measurements per frame. For this purpose, we parameterize the elliptic shape with its…
A product relative error estimation method for single index regression model is proposed as an alternative to absolute error methods, such as the least square estimation and the least absolute deviation estimation. It is scale invariant for…
In this paper, we develop a relative error bound for nuclear norm regularized matrix completion, with the focus on the completion of full-rank matrices. Under the assumption that the top eigenspaces of the target matrix are incoherent, we…
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…
We develop a variational multiscale proper orthogonal decomposition reduced-order model for turbulent incompressible Navier-Stokes equations. The error analysis of the full discretization of the model is presented. All error contributions…
Robust estimation of object poses in robotic manipulation is often addressed using foundational general estimators, that aim to handle diverse error sources naively within a single model. Still, they struggle due to environmental…
This paper addresses the challenge of probabilistic parameter estimation given measurement uncertainty in real-time. We provide a general formulation and apply this to pose estimation for an autonomous visual landing system. We present…
Customizing the precision of data can provide attractive trade-offs between accuracy and hardware resources. We propose a novel form of vector computing aimed at arrays of custom-precision floating point data. We represent these vectors in…
Mathematical models are used extensively for diverse tasks including analysis, optimization, and decision making. Frequently, those models are principled but imperfect representations of reality. This is either due to incomplete physical…