Abstract
The basic principle of interval arithmetic and the basic algorithm of the interval Newton methods are introduced. The prototype algorithm can not find any zero in an interval that has zero sometimes, that is, it is instable. So the prototype relaxation procedure is improved in this paper. Additionally, an immediate test of the existence of a solution following branch-and-bound is proposed, which avoids unwanted computations in those intervals that have no solution. The numerical results demonstrat that the improved interval Newton method is superior to prototype algorithm in terms of solution quality, stability and convergent speed.
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