超越方程的数值计算方法与收敛速度分析  

Analysis of Numerical Calculation Method and Convergence Rate of Transcendental Equation

作　　者：赵培玉[1] 吴素文[1] 冯大光[1] 于淼[1] 

机构地区：[1]沈阳农业大学理学院,辽宁沈阳110866

出　　处：《长江大学学报（自科版）（上旬）》2012年第5期1-2,5,共3页JOURNAL OF YANGTZE UNIVERSITY (NATURAL SCIENCE EDITION) SCI ＆ ENG

基　　金：国家自然科学基金项目(71001018)

摘　　要：二分法与迭代法是解决超越方程求根问题的主要数值计算方法。首先介绍了二分法,并在迭代法基本理论的基础上介绍了牛顿迭代法与埃特金加速迭代法;然后借助C语言分别采用二分法、牛顿迭代法、埃特金加速迭代法对一个超越方程进行数值了求解;最后对这3种方法的收敛速度进行了对比分析。结果表明,牛顿迭代法与埃特金加速迭代法收敛速度基本相同,二分法收敛速度最慢;求解超越方程的数值解法对于求解其他的方程求根问题具有一定的参考价值。Dichotomy and iterative methods are major methods for solving transcendental problem in numerical calculation. Firstly,the dichotomy is introduced and the Newton-iterative method and Aitken acceleration method are described based on the basic theory of iterative method;secondly,this three methods are adapted.to solve transcendental problem using C;lastly,convergence rate is compared by obtaining results.The results show that Newton-iterative method and Aitken acceleration method have same convergence rate,but convergence rate of dichotomy is slow.The numerical method for solving the transcendental problem has certain reference value to solve other equations.

关 键 词：超越方程:二分法 牛顿迭代法 埃特金加速迭代法 

分 类 号：O241[理学—计算数学]