Research ArticleOpen AccessGoogle Scholar indexed
Scanning and Selection Methods Using Solution Boxes of Inequality
- 1
Applied Mathematics·Volume 01 (2010)·Pages 520–528·Published 27 December 2010·DOI10.4236/am.2010.16069
Copy link · social · email
Abstract
Numerical methods often reduce solving a complicated problem to a set of elementary problems. In some previous papers, the author reduced the finding of solution boxes of a system of inequalities, the computation of integral value with error bound, the approximation of global maxima to computing solution boxes of one inequality. This paper contains new and improved methods for application of solution boxes of an inequality, furthermore the computational aspects are discussed in detail.
KeywordsInequalitySolution BoxScanning of Set
- F. Kálovics, “A New Tool: Solution Boxes of Inequality,” Journal of Software Engineering and Applications, Vol. 3, No. 8, 2010, pp. 737-745.
- R. Hammer, M. Hocks, U. Kulisch and D. Ratz, “Numerical Toolbox for Verified Computing”, Springer-Verlag, Berlin, 1993.
- F. Kálovics, “Zones and Integrals,” Journal of Computational and Applied Mathematics, Vol. 182, No. 2, 2005, pp. 243-251.
- F. Kálovics and G. Mészáros, “Box Valued Functions in Solving Systems of Equations and Inequalities,” Numerical Algorithms, Vol. 36, No. 1, 2004, pp. 1-12.
- F. Kálovics, “Solving Nonlinear Constrained Minimization Problems with a New Interval Valued Function,” Reliable Computing, Vol. 5, No. 4, 1999, pp. 395-406.