关键词: 指数函数多项式, 实根分离, 泰勒替换法, 区间列, 终止性

Abstract:

For addressing real root isolation problem of transcendental function polynomials， an interval isolation algorithm for exponential function polynomials named exRoot was proposed. In the algorithm， the real root isolation problem of non-polynomial real functions was transformed into sign determination problem of polynomial， then was solved. Firstly， the Taylor substitution method was used to construct the polynomial nested interval of the objective function. Then， the problem of finding the root of the exponential function was transformed into the problem of determining the positivity and negativity of the polynomial in the intervals. Finally， a comprehensive algorithm was given and applied to determine the reachability of rational eigenvalue linear system tentatively. The proposed algorithm was implemented in Maple efficiently and easily with readable output results. Different from HSOLVERand numerical calculation method fsolve， exRoot avoids discussing the existence of roots directly， and theoretically has termination and completeness. It can reach any precision and can avoid the systematic error brought by numerical solution when being applied into the optimization problem.

Key words: exponential function polynomial, real root isolation, Taylor substitution method, sequence of intervals, termination