Research on numerical solution of one-sided monotonic function dichotomy

Abstract

Aiming at the numerical solution problem of given interval dichotomy, the concept of one-sided monotonic function is proposed, and the unique existence of the solution is proved when the two ends of the function take different signs. Therefore, this significantly relaxes the discrimination conditions and effectively expands the numerical solution range of the dichotomy method. On this basis, it is proved that the one-sided monotonic function is a monotonic function in a relatively small interval containing the zero point. The introduction of the concept of one-sided monotonic function provides a theoretical basis for further expanding the application range of the dichotomy numerical solution, and has certain theoretical and practical significance for dealing with scientific and engineering problems as well as related numerical calculation problems.