Related papers: Mechanizing Olver's Error Arithmetic
In this study, we propose a novel extended target tracking algorithm which is capable of representing the extent of dynamic objects as an ellipsoid with a time-varying orientation angle. A diagonal positive semi-definite matrix is defined…
In machine learning, accurately predicting the probability that a specific input is correct is crucial for risk management. This process, known as uncertainty (or confidence) estimation, is particularly important in mission-critical…
In this paper, we develop a general approach for probabilistic estimation and optimization. An explicit formula and a computational approach are established for controlling the reliability of probabilistic estimation based on a mixed…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
Common practice in modern machine learning involves fitting a large number of parameters relative to the number of observations. These overparameterized models can exhibit surprising generalization behavior, e.g., ``double descent'' in the…
This paper discusses regularized estimators in the multivariate statistical model as tools naturally arising within a Bayesian framework. First, a link is established between Bayesian estimation and inference under parameter rounding…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
Researchers have developed neural network verification algorithms motivated by the need to characterize the robustness of deep neural networks. The verifiers aspire to answer whether a neural network guarantees certain properties with…
A widely used approximation of the Gaussian curvature on a triangulated surface is the angle defect, which measures the deviation between $2\pi$ and the sum of the angles between neighboring edges emanating from a common vertex. We show…
This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete,…
Detecting oriented objects along with estimating their rotation information is one crucial step for analyzing remote sensing images. Despite that many methods proposed recently have achieved remarkable performance, most of them directly…
In this paper, a new parametrization of the relative motion between two satellites orbiting a central body is presented. The parametrization is based on the nodal elements: a set of angles describing the orbit geometry with respect to the…
The demands of accuracy in measurements and engineering models today, renders the condition number of problems larger. While a corresponding increase in the precision of floating point numbers ensured a stable computing, the uncertainty in…
This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analyzes its convergence properties. It is established that…
In representations using frames, oblique duality appears in situations where the analysis and the synthesis has to be done in different subspaces. In some cases, we cannot obtain an explicit expression for the oblique duals and in others…
We present a computer assisted method for generating existence proofs and a posteriori error bounds for solutions to two point boundary value problems (BVPs). All truncation errors are accounted for and, if combined with interval arithmetic…
In the past four decades, research on count time series has made significant progress, but research on $\mathbb{Z}$-valued time series is relatively rare. Existing $\mathbb{Z}$-valued models are mainly of autoregressive structure, where the…
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In spite of being an integral part of bundle adjustment and…
We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important properties: the effectivity is close to unity with prescribed…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…