Geodesic
Approach to Solve the Set of Linear Algebraic Equations with Interval Uncertainty of Data Given
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 2, pp. 108-119

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The set of linear algebraic equations with interval matrixes of coefficients and interval right part is considered in the paper. The pseudosolution for such systems is introduced. The existence of pseudosolution for all interval sets of algebraic linear equations is proved in the paper, the way for pseudosolution analysis is shown on the basis of the solution the corresponding linear programming problem. It is necessary to use computation guaranteeing sufficient accuracy over standard data types of programming languages because of obtained problem degeneracy. Simplex method coupled with accurate rational-fractional computation gives effective solution to the problem. Coarse-grained parallelism for distributed computer systems with MPI is the instrument of realization. CUDA C software engineering is applied for accurate rational-fractional calculations.
Keywords: interval set of linear equations, linear programming
Mots-clés : pseudosolution of interval equation set, exact comtutations. 
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     author = {A. V. Panyukov and V. A. Golodov},
     title = {Approach to {Solve} the {Set} of {Linear} {Algebraic} {Equations} with {Interval} {Uncertainty} of {Data} {Given}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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A. V. Panyukov; V. A. Golodov. Approach to Solve the Set of Linear Algebraic Equations with Interval Uncertainty of Data Given. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 2, pp. 108-119. http://geodesic.mathdoc.fr/item/VYURU_2013_6_2_a7/