Inner and outer bounds for the solution set of parametric linear systems

DOI10.1016/j.cam.2005.08.048zbMath1108.65027OpenAlexW2035085214MaRDI QIDQ861892

Walter Krämer, Evgenija D. Popova

Publication date: 2 February 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.08.048

zbMATH Keywords

algorithmnumerical examplesinterval arithmeticenclosure methodC-XSCinner estimationfixed-point iteration methodparametric linear systemsvalidated software

Mathematics Subject Classification ID

Interval and finite arithmetic (65G30) Iterative numerical methods for linear systems (65F10) Algorithms with automatic result verification (65G20)

Related Items (17)

Parametric AE-solution sets to the parametric linear systems with multiple right-hand sides and parametric matrix equation \(A(p)X=B(p)\) ⋮ Enclosing the solution set of parametric interval matrix equation \(A(p)X = B(p)\) ⋮ Enclosures for the solution set of parametric interval linear systems ⋮ Fast enclosing the solution set of the parametric Sylvester matrix equations ⋮ High performance verified computing using C-XSC ⋮ The interval Lyapunov matrix equation: analytical results and an efficient numerical technique for outer estimation of the united solution set ⋮ Outer enclosures to the parametric \(AE\) solution set ⋮ Relations between various methods for solving linear interval and parametric equations ⋮ A new method for computing a \(p\)-solution to parametric interval linear systems with affine-linear and nonlinear dependencies ⋮ Efficient approaches for enclosing the united solution set of the interval generalized Sylvester matrix equations ⋮ Solvers for the verified solution of parametric linear systems ⋮ Results concerning interval linear systems with multiple right-hand sides and the interval matrix equation \(AX=B\) ⋮ Unnamed Item ⋮ Topological structure preserving numerical simulations of dynamical models ⋮ Real vector space of LR-fuzzy intervals with respect to the shape-preserving t-norm-based addition ⋮ Centered solutions for uncertain linear equations ⋮ Solving Linear Systems with Polynomial Parameter Dependency with Application to the Verified Solution of Problems in Structural Mechanics

Uses Software

• C-XSC
• C-XSC 2.0
• ParLinSys

Cites Work

• Fundamentals of SIGLA, an interval computing system over the completed set of intervals
• ANALYSIS OF MECHANICAL SYSTEMS USING INTERVAL COMPUTATIONS APPLIED TO FINITE ELEMENT METHODS
• Generalization of a Parametric Fixed-Point Iteration
• Rigorous Sensitivity Analysis for Systems of Linear and Nonlinear Equations
• Numerical Software with Result Verification
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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