Affiliation:
1. Navoi state
pedagogical institute
Abstract
Abstract
In this article we consider interval methods for solvingpoint (with real coefficients) and interval (with intervalcoefficients on the right side) systems of nonlinear algebraicequations. These methods are used to demonstrably solve pointsystems of nonlinear equations, as well as to find outer estimatesof the so-called united set of solutions to systems of nonlinearequations with interval coefficients. First, we will analyze theinterval methods of Newton and Krawczyk to show the advantages anddisadvantages of these and similar iterative methods. Next, wepropose a vertex method for outer estimation of solution sets ofinterval nonlinear systems, which also uses these iterativemethods. Here we limited ourselves only partially to intervalsystems. The proposed vertex method is more efficient where theconvergence of the iterative process is not guaranteed for theinterval iterative methods of Newton, Krawczyk or Hansen-Sengupta.The conducted numerical experiments show that the proposed vertexmethod gives more accurate estimates than the direct applicationof interval iterative methods.
Publisher
Research Square Platform LLC
Reference34 articles.
1. Alefeld, G. and Herzberger, J. (1983) Introduction to interval computations. Academic {P}ress, New {Y}ork
2. Neumaier, A. (1990) Interval methods for systems of equations. Cambridge University Press, Cambridge
3. Jaulin, L. and Kieffer, M. and Didrit, O. and Walter, E. (2001) Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics. Springer, London
4. Moore, R. E. and Kearfott, R. B. and Cloud, M. J. (2009) Introduction to interval analysis. SIAM, Philadelphia
5. Mayer, G. (2017) Interval Analysis and Automatic Result Verification. Walter de Gruyter, Berlin