Abstract
In this paper we apply the Γ -algorithm to obtain the feasibility conditions in different engineering problems involving a parametric system of linear inequalities. The feasibility conditions are the conditions for which the original system of linear inequalities has a solution. The Γ -algorithm is applied to solve the following problems: a heat transfer problem related to the finite difference method, various beam problems related to the finite difference method and a fracture mechanics problem related to numerical integration. Working with the Γ –algorithm, the feasibility conditions problem can be reduced to find the dual of a cone.
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References
Castillo, E., Cobo, A., Jubete, F., and Pruneda R. E. (1999).Orthogonal Sets and Polar Methods in Linear Algebra: Applications to Matrix Calculations,Systems of Equations and Inequalities, and Linear Programming. Wiley, New York.
Castillo, E., Conejo, A. J., Castillo, C. and Minguez, R. (2006). Solving ordinary differential equations with range conditions. Applications.SIAM Review, 48(2):307–307.
Castillo, E. and Jubete, F. (2004). The Ɖ - algorithm and some applications.International Journal of Mathematical Education in Science and Technology, 35(3):369–389.
Duffin, R. J. (1974). On Fourier’s analysis of linear inequality systems.Mathematical Programming Study, 1:71–95.
Ioakimidis, N. I. (2000). Derivation feasibility conditions in engineering problems under parametric inequality constraints with classical Fourier elimination.International Journal for Numerical Methods in Engineering, 48:1583–1599.
Ioakimidis, N. I. (2001). Finite differences/elements in classical beam problems: derivation of feasibility conditions under parametric inequality constraints with the help of Reduce and REDLOG.Computational Mechanics, 27:145–153.
Solares, C. and Chaves, E.W. V. (2006). Feasibility conditions with the Γ−algorithmin engineering problems.In Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (Ed., T.E. Simos), pp. 311–314, WILEY VCH, Weinheim.
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© 2008 Birkhäuser Boston
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Solares, C., Chaves, E.W. (2008). Feasibility Conditions in Engineering Problems Involving a Parametric System of Linear Inequalities. In: Advances in Mathematical and Statistical Modeling. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4626-4_25
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DOI: https://doi.org/10.1007/978-0-8176-4626-4_25
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