Related papers: Approximation in C^N
A problem is addressed of minimization of the number of measurements needed for digital image acquisition and reconstruction with a given accuracy. A sampling theory based method of image sampling and reconstruction is suggested that allows…
Model checking and testing are two areas with a similar goal: to verify that a system satisfies a property. They start with different hypothesis on the systems and develop many techniques with different notions of approximation, when an…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
This paper surveys hyperinterpolation, a quadrature-based approximation scheme. We cover classical results, provide examples on several domains, review recent progress on relaxed quadrature exactness, introduce methodological variants, and…
When expert systems based on causal probabilistic networks (CPNs) reach a certain size and complexity, the "combinatorial explosion monster" tends to be present. We propose an approximation scheme that identifies rarely occurring cases and…
Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of…
The wide application of estimation techniques in system analysis enable us to best determine and understand the history of system states. This paper attempts to delineate the theory behind linear and non-linear estimation with a suitable…
We give a basic overview of computational complexity, query complexity, and communication complexity, with quantum information incorporated into each of these scenarios. The aim is to provide simple but clear definitions, and to highlight…
Analytic approximations of functions of Cayley-Dickson variables are investigated. The case of functions of complexified Cayley-Dickson variables is also encompassed. Moreover, extensions of functions of Cayley-Dickson variables are…
Quickly moving to a new area of research is painful for researchers due to the vast amount of scientific literature in each field of study. One possible way to overcome this problem is to summarize a scientific topic. In this paper, we…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
We introduce the notion of {\it approximation type} for the partial, and in certain cases the total description of extensions of a given valuation from a field $K$ to the rational function field $K(x)$. To every extension, a unique…
When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be…
Many new database application domains such as experimental sciences and medicine are characterized by large sequences as their main form of data. Using approximate representation can significantly reduce the required storage and search…
We survey several results known on sampling in computational geometry.
Text Simplification (TS) aims to reduce the linguistic complexity of content to make it easier to understand. Research in TS has been of keen interest, especially as approaches to TS have shifted from manual, hand-crafted rules to automated…
In this master's thesis, we introduce expansion systems as a general framework to describe a large variety of approximation algorithms, such as Taylor approximation, decimal expansion and continued fraction. We consider some basic…
Artificial neural networks (ANNs) based machine learning models and especially deep learning models have been widely applied in computer vision, signal processing, wireless communications, and many other domains, where complex numbers occur…
This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct…