Jiří Rohn (1990)
Aplikace matematiky
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It is shown that if the concept of an interval solution to a system of linear interval equations given by Ratschek and Sauer is slightly modified, then only two nonlinear equations are to be solved to find a modified interval solution or to verify that no such solution exists.
Jean-Pierre Merlet (2009)
International Journal of Applied Mathematics and Computer Science
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Interval analysis is a relatively new mathematical tool that allows one to deal with problems that may have to be solved numerically with a computer. Examples of such problems are system solving and global optimization, but numerous other problems may be addressed as well. This approach has the following general advantages: (a) it allows to find solutions of a problem only within some finite domain which make sense as soon as the unknowns in the problem are physical parameters; (b) numerical...
Marian Mrozek, Piotr Zgliczyński (2000)
Annales Polonici Mathematici
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We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.
Jiří Taufer (1966)
Aplikace matematiky
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In this paper the method of factorization for boundary value problems of system of differential equations is generalized. The method described is successful providiny that the problem has a unique solution. Further the question of influence of errors resulting from numerical realization of the method on the solution is dealt with in the article.
Krämer, Walter (2007)
Serdica Journal of Computing
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The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006 The Maple Power Tool intpakX [24] de nes Maple types for real intervals and complex disc intervals. On the level of basic operations, intpakX includes the four basic arithmetic operators, including extended interval division as an extra function. Furthermore, there are power, square, square root, logarithm and exponential functions, a set of standard...
Günter Mayer (1989)
Aplikace matematiky
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We present a class of Newton-like methods to enclose solutions of systems of nonlinear equations. Theorems are derived concerning the feasibility of the method, its global convergence, its speed and the quality of enclosure.