Related papers: Interval Linear Algebra
A linear inference is a valid inequality of Boolean algebra in which each variable occurs at most once on each side. In this work we leverage recently developed graphical representations of linear formulae to build an implementation that is…
This article is meant to give a lucid and widely accessible, self-contained account of a novel way of performing arithmetic operations on fuzzy intervals. Based on two formulae of generalized inversion (the first in close analogy to the…
This report showcases the role of, and future directions for, the field of Randomized Numerical Linear Algebra (RNLA) in a selection of scientific applications. These applications span the domains of imaging, genomics and dynamical systems,…
There is strong interest in developing mathematical methods that can be used to understand complex neural networks used in image analysis. In this paper, we introduce techniques from Linear Algebra to model neural network layers as maps…
In the last quarter of a century, algebraic statistics has established itself as an expanding field which uses multilinear algebra, commutative algebra, computational algebra, geometry, and combinatorics to tackle problems in mathematical…
This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The…
This is a replacement paper. There are 6 chapters. The first two chapters are introductory. The third chapter is on extremal graph theory. The fourth chapter is about algebra in graph theory. The fifth chapter is focused on algorithms. The…
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and…
We give a survey of work on the number of vertices of the convex hull of integer points defined by the system of linear inequalities. Also, we present our improvement of some of these.
We introduce a new framework called linear algebraic number theory (LANT) that reformulates the number-theoretic problem as a regression model and solves it using matrix algebra. This framework restricts all computations to log space,…
The main purpose of this book is to propose an introduction to the modern tools of algebraic complexity. To remain as simple as possible while providing meaningful examples, we chose to focus on effective linear algebra; this is certainly…
This book gives the basic notions of fuzzy matrix theory and its applications to simple fuzzy models. The approach is non-traditional in order to attract many students to use this methodology in their research. The traditional approach of…
The book is structured into four main chapters. Chapter 1 introduces the foundational concepts of divergence measures, including the well-known Kullback-Leibler divergence and its limitations. It then presents a detailed exploration of…
Complex interval arithmetic is a powerful tool for the analysis of computational errors. The naturally arising rectangular, polar, and circular (together called primitive) interval types are not closed under simple arithmetic operations,…
Concise introduction to a relatively new subject of non-linear algebra: literal extension of text-book linear algebra to the case of non-linear equations and maps. This powerful science is based on the notions of discriminant…
In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…
The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the…
Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages) do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…