Editor‘s Note: Tang poems were a zenith of ancient Chinese Iiterature, and their splendor has since been rarelyequaled. Mang Chinese still recite Tang poetrg to this day In this issue, we are pleased to publish two p...Editor‘s Note: Tang poems were a zenith of ancient Chinese Iiterature, and their splendor has since been rarelyequaled. Mang Chinese still recite Tang poetrg to this day In this issue, we are pleased to publish two poemswritten by Li Bai, a poet of the Tang Dunasty (618-907), translated by Mr. N.C Doo a Chinese British.展开更多
It is well known that Newton’s method xn+1=u（xn） Vn∈|No, where u（x）=x-P’（x）-1P（x）, is widely used in solving nonlinear equations P（x）=0 and each kind of its improvement depends on the generalizing iterati...It is well known that Newton’s method xn+1=u（xn） Vn∈|No, where u（x）=x-P’（x）-1P（x）, is widely used in solving nonlinear equations P（x）=0 and each kind of its improvement depends on the generalizing iteration function u（x） to w（x,z）=x-P’（z）-1P（x）. The method xn+1=w（xn,1/2（xn+yn））, y（n+1）=w(xn+1,1/2（xn+yn）) which has been proposed by King （Numer. Math., 18 （1972）, 298） and again by Werner （Numer. Math., 32 （1979）, 333） recently is convergent with order 1+21/2. AS a iteration method which can be applied directly to systems of nonlinear equations it is so remarkable that its convergence order is increased so much and yet it only needs as many function evaluations as that of Newton’s method. Owing to the fast展开更多
文摘Editor‘s Note: Tang poems were a zenith of ancient Chinese Iiterature, and their splendor has since been rarelyequaled. Mang Chinese still recite Tang poetrg to this day In this issue, we are pleased to publish two poemswritten by Li Bai, a poet of the Tang Dunasty (618-907), translated by Mr. N.C Doo a Chinese British.
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文摘It is well known that Newton’s method xn+1=u（xn） Vn∈|No, where u（x）=x-P’（x）-1P（x）, is widely used in solving nonlinear equations P（x）=0 and each kind of its improvement depends on the generalizing iteration function u（x） to w（x,z）=x-P’（z）-1P（x）. The method xn+1=w（xn,1/2（xn+yn））, y（n+1）=w(xn+1,1/2（xn+yn）) which has been proposed by King （Numer. Math., 18 （1972）, 298） and again by Werner （Numer. Math., 32 （1979）, 333） recently is convergent with order 1+21/2. AS a iteration method which can be applied directly to systems of nonlinear equations it is so remarkable that its convergence order is increased so much and yet it only needs as many function evaluations as that of Newton’s method. Owing to the fast
