1、大规模矩阵问题的大规模矩阵问题的Krylov 子空间方法综述子空间方法综述K(L)X(0)X(1)KLX(0)X(1)TW AV1(0)()TTyW AVW r(0)()0TWrAVy(1)(0)1(0)()TTxxV W AVW r(1)()min( )(0)xzzx K1/2( )( (),)zA xz xz(0)(1)()min( )z xxzK1/22( )(,)zbAzbAz bAz(0)(0)(0)2(0)(0)( ,),AmA rspan rArA rrm -1，Kdim( , )min , mA vmK(, )mA vK(1)1/ 2( , )vvv v( )( )(1)(2)
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5、VKfunction x=cg(A,b,tol)t=cputime;n = numel(b);x0=rand(n,1)r=b-A*x0;s=b-A*x0;x=x0;j=1;while (norm(r)tol) count(j)=j-1; res(j)=norm(r); alpha(j)=dot(r,r)/dot(s,(A*r);b1=dot(r,r); (续续)x=x+(alpha(j)*s;r=r-(alpha(j)*(A*s);b2=dot(r,r);beta(j+1)=b2/b1;s=r+(beta(j+1)*s; j=j+1;end t=cputime-tplot(count,res),xlabel(迭代步迭代步),ylabel(残量残量),title(残量随迭代步的变化残量随迭代步的变化),set(findobj(gca,Type,line,Color,0 0 1),.Color,red,.LineWidth,2)
