Enclosing the solution set of parametric interval matrix equation \(A(p)X = B(p)\)

DOI10.1007/s11075-017-0382-1zbMath1391.65132OpenAlexW2741922630MaRDI QIDQ1646665

Evgenija D. Popova

Publication date: 25 June 2018

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-017-0382-1

zbMATH Keywords

interval parameterslinear matrix equationssolution enclosure

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Iterative numerical methods for linear systems (65F10) General methods in interval analysis (65G40)

Related Items (7)

Linear constraint problem of Hermitian unitary symplectic matrices ⋮ New parameterized solution with application to bounding secondary variables in FE models of structures ⋮ Proving endpoint dependence in solving interval parametric linear systems ⋮ Rank one interval enclosure of the parametric united solution set ⋮ On preconditioning and solving an extended class of interval parametric linear systems ⋮ Algebraic solution to interval equilibrium equations of truss structures ⋮ Enclosing the solution set of the parametric generalised Sylvester matrix equation A(p)XB(p) + C(p)XD(p) = F(p)

Uses Software

• ParLinSys

Cites Work

• Unnamed Item
• Parametric AE-solution sets to the parametric linear systems with multiple right-hand sides and parametric matrix equation \(A(p)X=B(p)\)
• Results concerning interval linear systems with multiple right-hand sides and the interval matrix equation \(AX=B\)
• Explicit description of 2D parametric solution sets
• Interval linear systems with symmetric matrices, skew-symmetric matrices and dependencies in the right hand side
• 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
• Linear systems with large uncertainties, with applications to truss structures
• A note on epsilon-inflation
• A method for outer interval solution of linear parametric systems
• Visualizing parametric solution sets
• Improved enclosure for some parametric solution sets with linear shape
• Verification methods: Rigorous results using floating-point arithmetic
• Enclosures for the solution set of parametric interval linear systems
• Generalization of a Parametric Fixed-Point Iteration
• A Comparison of Methods for Solving Parametric Interval Linear Systems with General Dependencies
• Interval Methods for Systems of Equations
• Computing Exact Componentwise Bounds on Solutions of Lineary Systems with Interval Data is NP-Hard

This page was built for publication: Enclosing the solution set of parametric interval matrix equation \(A(p)X = B(p)\)