SOFTWARE OF SEPARATION OF ROOTS ON A SEGMENT
Abstract
All known widespread algorithms of a numerical solution of an equation on a straight line segment assume that segments of isolation of roots are already known. These are such segments, on each of which a solution is one and only one. The method of this work allows to discover all solutions of an equation f(x) = 0 for arbitrary continuously differentiable function f(x) on the set segment of a straight line with the set accuracy. Convergence of the method is exponential. Thus, the method automatically separates roots. In the course of numerical methods it hits in its ideological center, forcing to consider all structure of the theory to make it clear and deepen its understanding. The method of this work is realized in a desktop in language Java.
Downloads
Metrics
References
1. Berezyn, I. S. & Zhydkov, N. P. (1966). Methods of calculation (t.1). Moscow: “Nauka”.
2. Tproger (2018). Everything for learning Java. Examples of development. Retrieved from https://tproger.ru/tag/java.
3. Veitsblit, O. Y. (2011). Methods of calculation. Methodical recommendations for laboratory work. Kherson: Ailant.
4. Ryd, M. & Saimon, B. (1977). Methods of modern mathematical physics (t.1). Moscow: Myr.
5. Veitsblit, O. Y. (2011). Methods of calculation. Tutorial. Kherson: Ailant.
6. Bakhvalov, N. S. (1973). Numerical methods (t.1). Moscow: “Nauka”.
7. Arnold, V. Y. (1978). Additional chapters of the theory of ordinary differential equations. Moscow: “Nauka”.
8. Kalman, D. (2002). Doubly Recursive Multivariate Automatic Differentiation. Magazine Mathematics, 75 (3), 187-202.
9. JFreeChart. (2013). Downloading JFreeChart. Retrieved from http://www.jfree.org/jfreechart/download.html.