Computing Exact Componentwise Bounds on Solutions of Linear Systems with Interval Data isNP-Hard
SIAM Journal on Matrix Analysis and Applications
Subdivision Direction Selection in Interval Methods for Global Optimization
SIAM Journal on Numerical Analysis
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
A Generalized Interval Arithmetic
Proceedings of the International Symposium on Interval Mathemantics
Efficient Interval Methods for Finite Element Solutions
HPCS '02 Proceedings of the 16th Annual International Symposium on High Performance Computing Systems and Applications
Parametric Linear System of Equations, Whose Elements are Nonlinear Functions
SCAN '06 Proceedings of the 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
Solving linear systems whose input data are rational functions of interval parameters
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
On checking the monotonicity of parametric interval solution of linear structural systems
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
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An interval global optimization method combined with the Direct Method for solving parametric linear systems is used for computing a tight enclosure for the solution set of parametric linear system whose input data are non-linear functions of interval parameters. Revised affine arithmetic is used to handle the nonlinear dependencies. The Direct Method performs the monotonicity test to speed up the convergence of the global optimization. It is shown that the monotonicity test significantly increases the convergence of the global optimization method. Some illustrative examples are solved by the discussed method, and the results are compared to literature data produces by other methods.