摘要
In this paper an interval verification algorithm for the solutions of nonlinear systems is presented. The algorithm combines the high convergent speed of the floating-point iterative methods and the rigorous inclusion property of the interval methods. By using the so-called epsilon-inflation, .the algorithm might be reliably used to solve various nonlinear systems, and the sufficiently rigorous error bounds of the solution could also be produced.Besides, a verification algorithm given by G. Mayer is also discussed. A Mayer’s open question is answered negatively by constructing a simple counterexample, and a new conjecture about this algorithm is presented by the author.
In this paper an interval verification algorithm for the solutions of nonlinear systems is presented. The algorithm combines the high convergent speed of the floating-point iterative methods and the rigorous inclusion property of the interval methods. By using the so-called epsilon-inflation, .the algorithm might be reliably used to solve various nonlinear systems, and the sufficiently rigorous error bounds of the solution could also be produced.Besides, a verification algorithm given by G. Mayer is also discussed. A Mayer's open question is answered negatively by constructing a simple counterexample, and a new conjecture about this algorithm is presented by the author.
出处
《数值计算与计算机应用》
CSCD
北大核心
1998年第2期107-117,共11页
Journal on Numerical Methods and Computer Applications
