scholarly journals Analyzing linear systems containing strict inequalities via evenly convex hulls

2006 ◽  
Vol 169 (3) ◽  
pp. 1079-1095 ◽  
Author(s):  
Miguel A. Goberna ◽  
Margarita M.L. Rodrı́guez
Keyword(s):  
Linear Systems ◽  
Convex Hulls ◽  
Strict Inequalities

Evenly Convex Polyhedra: Finite Linear Systems Containing Strict Inequalities

2020 ◽  
pp. 61-99
Author(s):  
María D. Fajardo ◽  
Miguel A. Goberna ◽  
Margarita M. L. Rodríguez ◽  
José Vicente-Pérez
Keyword(s):  
Linear Systems ◽  
Convex Polyhedra ◽  
Strict Inequalities ◽  
Finite Linear

scholarly journals On linear systems containing strict inequalities

2003 ◽  
Vol 360 ◽  
pp. 151-171 ◽  
Author(s):  
Miguel A. Goberna ◽  
Valentín Jornet ◽  
Margarita M.L. Rodríguez
Keyword(s):  
Linear Systems ◽  
Strict Inequalities

scholarly journals On Finite Linear Systems Containing Strict Inequalities

2017 ◽  
Vol 173 (1) ◽  
pp. 131-154
Author(s):  
Margarita M. L. Rodríguez ◽  
José Vicente-Pérez
Keyword(s):  
Linear Systems ◽  
Strict Inequalities ◽  
Finite Linear

Evenly Convex Sets: Linear Systems Containing Strict Inequalities

2020 ◽  
pp. 1-60
Author(s):  
María D. Fajardo ◽  
Miguel A. Goberna ◽  
Margarita M. L. Rodríguez ◽  
José Vicente-Pérez
Keyword(s):  
Linear Systems ◽  
Convex Sets ◽  
Strict Inequalities

Reserve of characteristic inclusion for interval linear systems of relations

2021 ◽  
pp. 61-85
Author(s):  
Ирина Александровна Шарая ◽  
Сергей Петрович Шарый
Keyword(s):  
Linear Systems ◽  
Interval Arithmetic ◽  
Quantitative Measure ◽  
Solution Set ◽  
Special Cases ◽  
Interval Linear ◽  
Strict Inequalities ◽  
Interval Linear Systems ◽  
Interval Systems ◽  
Linear Systems Of Equations

В работе рассматриваются интервальные линейные включения Cx ⊆ d в полной интервальной арифметике Каухера. Вводится количественная мера выполнения этого включения, названная “резервом включения”, исследуются ее свойства и приложения. Показано, что резерв включения оказывается полезным инструментом при изучении АЕ-решений и кванторных решений интервальных линейных систем уравнений и неравенств. В частности, использование резерва включения помогает при определении положения точки относительно множества решений, при исследовании пустоты множества решений или его внутренности и т.п In this paper, we consider interval linear inclusions Cx ⊆ d in the Kaucher complete interval arithmetic. These inclusions are important both on their own and because they provide equivalent and useful descriptions for the so-called quantifier solutions and AE-solutions to interval systems of linear algebraic relations of the form Ax σ b , where A is an interval m × n -matrix, x ∈ R , b is an interval m -vector, and σ ∈ {= , ≤ , ≥} . In other words, these are interval systems in which equations and non-strict inequalities can be mixed. Considering the inclusion Cx ⊆ d in the Kaucher complete interval arithmetic allows studing simultaneously and in a uniform way all the different special cases of quantifier solutions and AE-solutions of interval systems of linear relations, as well as using interval analysis methods. A quantitative measure, called the “inclusion reserve”, is introduced to characterize how strong the inclusion Cx ⊆ d is fulfilled. In our work, we investigate its properties and applications. It is shown that the inclusion reserve turns out to be a useful tool in the study of AE-solutions and quantifier solutions of interval linear systems of equations and inequalities. In particular, the use of the inclusion reserve helps to determine the position of a point relative to a solution set, in investigating whether the solution set is empty or not, whether a point is in the interior of the solution set, etc

Well-Posed Linear Systems

2005 ◽  
Author(s):  
Olof Staffans
Keyword(s):  
Linear Systems ◽  
Well Posed

Principles of Linear Systems

1997 ◽  
Author(s):  
Philip E. Sarachik
Keyword(s):  
Linear Systems

Particularities of overdetermined linear systems arising in particle size analysis

1992 ◽  
Vol 2 (8) ◽  
pp. 1547-1555
Author(s):  
D. M. Calistru ◽  
R. Mondescu ◽  
I. Baltog
Keyword(s):  
Particle Size ◽  
Linear Systems ◽  
Particle Size Analysis ◽  
Size Analysis ◽  
Overdetermined Linear Systems
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