Outer enclosures to the parametric \(AE\) solution set

DOI10.1007/s00500-013-1011-0zbMath1327.65084OpenAlexW2020784316MaRDI QIDQ889879

Milan Hladík, Evgenija D. Popova

Publication date: 9 November 2015

Published in: Soft Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00500-013-1011-0

zbMATH Keywords

numerical examplelinear programminglinear systemsinterval arithmeticdependent datatolerable solution setcontrollable solution set\(AE\) solution setBauer-Skeel method

Mathematics Subject Classification ID

Related Items (25)

AE solutions to two-sided interval linear systems over max-plus algebra ⋮ Improved enclosure for some parametric solution sets with linear shape ⋮ Parametric AE-solution sets to the parametric linear systems with multiple right-hand sides and parametric matrix equation \(A(p)X=B(p)\) ⋮ Inner estimation of the parametric tolerable solution set ⋮ Robust optimal solutions in interval linear programming with forall-exists quantifiers ⋮ Farkas-type conditions of general interval linear systems for AE solvability ⋮ Fast enclosing the solution set of the parametric Sylvester matrix equations ⋮ Generalized solutions to interval linear programmes and related necessary and sufficient optimality conditions ⋮ A new methodology for solving fuzzy systems of equations: thick fuzzy sets based approach ⋮ Manifestation of interval uncertainties for fractional differential equations under conformable derivative ⋮ Extremal Results for Algebraic Linear Interval Systems ⋮ Transformations of interval linear systems of equations and inequalities ⋮ Necessary and sufficient conditions of some strong optimal solutions to the interval linear programming ⋮ AE solutions and AE solvability to general interval linear systems ⋮ Parameterized outer estimation of \(AE\)-solution sets to parametric interval linear systems ⋮ Solving over-constrained systems of non-linear interval equations -- and its robotic application ⋮ Parametric functional representation of interval number with arithmetic operations ⋮ Checking strong optimality of interval linear programming with inequality constraints and nonnegative constraints ⋮ On preconditioning and solving an extended class of interval parametric linear systems ⋮ Solvability and feasibility of interval linear equations and inequalities ⋮ Farkas-type theorems for interval linear systems ⋮ AE solutions to interval linear systems over max-plus algebra ⋮ EA solutions and EA solvability to general interval linear systems ⋮ On the unbounded parametric tolerable solution set ⋮ Enclosing the solution set of the parametric generalised Sylvester matrix equation A(p)XB(p) + C(p)XD(p) = F(p)

Uses Software

• Matlab
• ParLinSys

Cites Work

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• A method for outer interval solution of systems of linear equations depending linearly on interval parameters
• Inner and outer bounds for the solution set of parametric linear systems
• Controllable solution set to interval static systems
• Linear interval tolerance problem and linear programming techniques
• A new technique in systems analysis under interval uncertainty and ambiguity
• A right-preconditioning process for the formal-algebraic approach to inner and outer estimation of AE-solution sets.
• Solution sets of interval-valued fuzzy relational equations
• Enclosures for the solution set of parametric interval linear systems
• Robust stability of positive continuous-time linear systems with delays
• Explicit Description of AE Solution Sets for Parametric Linear Systems
• Linear Optimization Problems with Inexact Data

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