计算方法方程迭代法教学课件-002

●●第一章方程求根杨娟合肥工业大学计算机学院Valadononry.chAsposeslidesforNET4odientPEvaluationonly.CreatedwithAsposeSlidesforNET4.0dientProfilo71Copyright2019-2019AsposePtyL提纲o二分法o迭代法o迭代过程的加速o牛顿法Valadononry.chAsposeslidesforNET4odientPEvaluationonly.CreatedwithAsposeSlidesforNET4.0dientProfilo71Copyright2019-2019AsposePtyL二分法设∫(a)·f(b)<0,取x0=(a+b)/2假如f(x)是(x)的零点那么输出x0,停止假若不然y=f(x)若f(a)与f(x)同号,则a1=x0,=b否则a1=a,b1=x00分过程中有三个量在(区间、近似根、区间长度)(1)[a2b=[a12b1]lak,bb1-a4a.tb2(3)b-a,bb-abEvaluauononr.chAsposeslidesforNET4odientPEvaluationonly.CreatedwithAsposeSlidesforNET4.0dientProfilo71Copyright2019-2019AsposePtyL二分法收敛性分析因|x-x*k(b2-a2)/2=(b-a)/2故有,x=(a2+b2)/2→x*(k→>∞)因此,只要二分的足够多次(即k充分大),便有x-x<这里8为预定的精度Valadononry.chAsposeslidesforNET4odientPEvaluationonly.CreatedwithAsposeSlidesforNET4.0dientProfilo71Copyright2019-2019AsposePtyL二分法例1求f(x)=x3-x-1=0在[01.5内的一个实根,准确到小数点后2位Valadononry.chAsposeslidesforNET4odientPEvaluationonly.CreatedwithAsposeSlidesforNET4.0dientProfilo71Copyright2019-2019AsposePtyL二分法arf(X)符号01.01.51.2511.251.3751.3751.312523451.31251.34381.34381.32811.32811.320361.32031.3242只要二分6次(k=6),便能达到预定的x-x6|≤005Valadononry.chAsposeslidesforNET4odientPEvaluationonly.CreatedwithAsposeSlidesforNET4.0dientProfilo71Copyright2019-2019AsposePtyL二分法二分法的优点是算法简单,且总是收敛的,缺点是收敛太慢,故一般不单独将其用于求根,只用其为根求得一个较好的近似值Valadononry.chAsposeslidesforNET4odientPEvaluationonly.CreatedwithAsposeSlidesforNET4.0dientProfilo71Copyright2019-2019AsposePtyL提纲o二分法o迭代法o迭代过程的加速o牛顿法Valadononry.chAsposeslidesforNET4odientPEvaluationonl