Related papers: A new discrepancy principle

A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy…

The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work…

A discrepancy principle for solving nonlinear equations with monotone operators given noisy data is formulated. The existence and uniqueness of the corresponding regularization parameter $a(\delta)$ is proved. Convergence of the solution…

We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right hand side are available. A natural approach is to take the average of the measurements as an approximation of the…

Disagreement between two classifiers regarding the class membership of an observation in pattern recognition can be indicative of an anomaly and its nuance. As in general classifiers base their decision on class aposteriori probabilities,…

We study a unified approach and algorithm for constructive discrepancy minimization based on a stochastic process. By varying the parameters of the process, one can recover various state-of-the-art results. We demonstrate the flexibility of…

Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) divided differences.

Often it is desirable to stabilize a system around an optimal state. This can be effectively accomplished using feedback control, where the system deviation from the desired state is measured in order to determine the magnitude of the…

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

Based on the principle of causality, I advance a new principle of variation and try to use it as the most general principle for research into laws of nature.

A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…

In this paper we revisit the discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems in Hilbert spaces and provide some new and improved saturation results under less restrictive conditions, comparing with the…

While explainability is a desirable characteristic of increasingly complex black-box models, modern explanation methods have been shown to be inconsistent and contradictory. The semantics of explanations is not always fully understood - to…

These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…

A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…

In this note, we prove a new uncertainty principle for functions with radial symmetry by differentiating a radial version of the Stein-Weiss inequality. The difficulty is to prove the differentiability in the limit of the best constant…

This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…

It is generally assumed that any discrepancy between an object's inertial and gravitational masses, leading to a violation of the equivalence principle, arises from the nature of its internal constituents and their interactions. We show…

In literature, the central limit theorems for the product of sums of various random variables have studied. The purpose of this note is to show that this kind of results are corollary of the invariance principle.

We propose a criterion of equidistribution by the differentiability of certain arithmetic invariants. Combined with the slope method and the asymptotic measures, this criterion gives a new "conceptual" proof to equidistribution results…