湖南师范大学自然科学学报
湖南師範大學自然科學學報
호남사범대학자연과학학보
ACTA SCIENTIARUM NATURALIUM UNIVERSITATIS NORMALIS HUNANENSIS
2009年
4期
10-13
,共4页
Newton场线微分方程%场线法%非线性方程组%求所有根
Newton場線微分方程%場線法%非線性方程組%求所有根
Newton장선미분방정%장선법%비선성방정조%구소유근
Newton field-line differential equation%field-line algorithm%nonlinear system of equations%finding all roots
为求解非线性方程组F(x)=0,提出Newton场线微分方程x_t(t)=-(DF(x))~(-1)F(x),x(0)=x~0.在m重根x~*的中心场域中任取初始点x~0,证明了用前向Euler格式得到的解序列x~n一定收敛到此根,故场线法大范围收敛.由此提出求非线性方程组所有根的场线算法,其有效性为数值试验所证实.
為求解非線性方程組F(x)=0,提齣Newton場線微分方程x_t(t)=-(DF(x))~(-1)F(x),x(0)=x~0.在m重根x~*的中心場域中任取初始點x~0,證明瞭用前嚮Euler格式得到的解序列x~n一定收斂到此根,故場線法大範圍收斂.由此提齣求非線性方程組所有根的場線算法,其有效性為數值試驗所證實.
위구해비선성방정조F(x)=0,제출Newton장선미분방정x_t(t)=-(DF(x))~(-1)F(x),x(0)=x~0.재m중근x~*적중심장역중임취초시점x~0,증명료용전향Euler격식득도적해서렬x~n일정수렴도차근,고장선법대범위수렴.유차제출구비선성방정조소유근적장선산법,기유효성위수치시험소증실.
To find all roots of nonlinear equation system F(x)=0,Newton field-line differential equation x_t(t)=-(DF(x))~(-1)F(x),x(0)=x~0 is proposed.It is proved that taking any initial point x~0 in central field domain of m-ple root x~*,the solution series{x~n}computed by forward Euler scheme certainly converges to the root x~*.The field.1ine method is globally convergent.Then a field-line algorithm for finding all roots of nonlinear equation system is proposed.Its efficiency is shown by numberical experiments.
