求N+1次勒讓德多項式的m(m=0,1,...)階導數零點Matlab程序

子程序：

function?x=jp(N,alpha,beta)

n=1:N;

a(1)=(alpha+beta+2)/2;

b(1)=(beta-alpha)/2;

a([2:N+1])=(2*n+alpha+beta+1).*(2*n+alpha+beta+2)./(2*(n+1).*(n+alpha+beta+1));

b([2:N+1])=(alpha*alpha-beta*beta)*(2*n+alpha+beta+1)./(2*(n+1).*(n+alpha+beta+1).*(2*n+alpha+beta));

c=(n+alpha).*(n+beta).*(2*n+alpha+beta+2)./((n+1).*(n+alpha+beta+1).*(2*n+alpha+beta));

A=diag(b./a)+diag(1./a([1:N]),1)+diag(c./a([2:N+1]),-1);

x=sort(eig(A))'

主程序

function?x=djp(N,alpha,beta,m)

N1=N-m;

alpha1=alpha+m;

beta1=beta+m;

x=jp(N1,alpha1,beta1)

說明：alpha,beta都取0，m表示m階導數。

比如求5次勒讓德多項式1階導數的零點

>>?djp(4,0,0,1)?回車

x?=

-0.7651???-0.2852????0.2852????0.7651

又如求10次勒讓德多項式的零點

>>?djp(9,0,0,0)

x?=

-0.9739???-0.8651???-0.6794???-0.4334???-0.1489????0.1489????0.4334????0.6794????0.8651????0.9739

又如求10次勒讓德多項式4階導數的零點

>>?djp(9,0,0,4)

x?=

-0.7374???-0.4689???-0.1609????0.1609????0.4689????0.7374

◆◆

評論讀取中....

請登錄后再發表評論!

◆◆

修改失敗，請稍后嘗試