亲测可用雅克比高斯塞尔德SOR求迭代次数

【亲测可用】雅克比、高斯塞尔德、SOR求迭代次数%雅克比m文件functionx=Jacobi(A,b)x0=ones(size(b));n=25;%最大迭代次数ee=0.00001;%青度n1=length(b);x1=zeros(n1,1);fori=1:nforj=1:n1s=0;fork=1:n1ifk~=js=s+A(j,k)*x0(k);endendendifnorm(x1-x0)<eebreakendx0=x1;endx=x1;%主界面A=[4,-1,0,-1,0,0;-1,4,-1,0,-1,0;0,-1,4,0,0,-1;-1,0,0,4,-1,0;0,-1,0,-1,4,-1;0,0,-1,0,-1,4];b=[0,5,0,6,-2,6]';x=Jacobi(A,b)%高斯赛尔德m文件functionx=GS(A,b,x0,tol)if(nargin==2)x0=ones(size(b));tol=0.00001;tol=0.00001；elsesprintf('USAGE:Gauss_Seidel(A,b,x0,tol)')endD=diag(diag(A));U=triu(A,1);L=tril(A,-1);G=-(D+L)\U;d1=(D+L)\b;x=G*x0+d1;n=1;whilenorm(x-x0)>=tolx0=x;x=G*x0+d1;n=n+1;endn%主界面A=[4,-1,0,-1,0,0;-1,4,-1,0,-1,0;0,-1,4,0,0,-1;-1,0,0,4,-1,0;0,-1,0,-1,4,-1;0,0,-1,0,-1,4];x=GS(A,b)%SOR^tm文件function[x,k]=EqtsSOR(A,b,x0,omiga,eps)%超松弓(SOB迭代法求解线性方程组Ax=b%[xk]=EqtsSOR(A,b,x0,eps)%x!S向量，列向量%女迭代次数%A:系数矩阵%b:列向量%x0迭代初始值，列向量%omiga松弛因子，可缺省，缺省值为1,即为GS迭代法%eps误差限ifnargin==4eps=0.00001;endifnargin==3omiga=1;eps=0.00001;endifnargin==2x0=ones(size(b));omiga=1;eps=0.00001;end%佥查输入参数n=length(b);ifsize(A,1)~=n|n~=length(x0)disp('输入参数有误！');x='';k='';return;end%迭代求解k=0;x=zeros(n,1);while1k=k+1;fori=1:nz=z+A(i,j)*x(j);endforj=i+1:nz=z+A(i,j)*x0(j);endx(i)=(1-omiga)*x0(i)+omiga*(b(i)-z)/A(i,i);endif(norm(x-x0)<=eps)|(k==25)break;endx0=x;endifk==25disp('迭代次数太多！')x='';endreturn;%SORi界面A=[4,-1,0,-1,0,0;-1,4,-1,0,-1,0;0,-1,4,0,0,-1;-1,0,0,4,-1,0;0,-1,0,-1,4,-1;0,0,-1,0,-1,4];b=[0,5,0,6,-2,6]';x0=ones(size(b));omiga=1.1;eps=0.00005;[xk]=EqtsSOR(A,b,x0,omiga,eps)%SO越彳tm文件(备用)function[y,k,v]=sor(A,b,x,w,tol,M)%x为迭代初值，w为松弛因子(0<w<2),tol为允许误差,%v为标志变量，M为最大迭代次数D=diag(diag(A));L=tril(A,-1);U=triu(A,1);L1=D+w*L;G1=((1-w)*D-w*U);d=w*b;

v=0;k=0;while1b=G1*x+d;y=inv(L1)*b;e=norm(y-x,inf);x=y;ife<=tolv=1;break;endk=k+1;ifk>Mbreakendendfunctiony=fSOR(A,b,x,h,eps,M)w=0:h:2;n=2/h+1;%n=2/h+1;%松弛因子w的个数K=zeros(1,n);fori=1:n[x,K(i),index]=sor(A,b,x,w(i),eps,M);endK;scatter(w,K,'filled','r')%绘制迭代