1、 fun1=inline(x3-x-1); x0,k=bisect1(fun1,1.3,1.4,1e-4)x0 =1.3247k =7简单迭代法function x0,k=iterate1(fun1,x0,ep,N)N=500;3x=x0;x0=x+2*ep;while abs(x-x0)ep & k0表示收敛,h A=2 3 4;3 5 2;4 3 30; b=6,5,32b = 6 5 32 A,x=gauss3(A,b)A = 2.0000 3.0000 4.0000 6.0000 0 0.5000 -4.0000 -4.0000 0 0 -2.0000 -4.0000 -13 8 2列
2、选主元的高斯消元法:function A,x=gauss5(A,b)%本算法用列选主元的高斯消元法求解线性方程组 %选主元 ap,p=max(abs(A(k:n,k); p=p+k-1; if pk t=A(k,: A(k,:)=A(p,: A(p,:)=t; %消元 A(k+1): A(k+1): end%回代 x=zeros(n,1);n)*x(sk+1:; A,x=gauss5(A,b) 4.0000 3.0000 30.0000 32.0000 0 2.7500 -20.5000 -19.0000 0 0 0.1818 0.3636三角分解法:Doolittle 分解function
3、L,U=doolittle1(A)n=length(A);U=zeros(n);L=eye(n);U(1,:)=A(1,:L(2:n,1)=A(2:n,1)/U(1,1);for k=2:n U(k,k:n)=A(k,k:n)-L(k,1:k-1)*U(1:k-1,k:n); L(k+1:n,k)=A(k+1:n,k)-L(k+1:n,1:k-1,n)/U(k,k);Endy=zeros(n,1);x=y;y(1)=b(1);for i=2: y(i)=b(i)-L(i,1:i-1)*y(1:i-1);x(n)=y(n)/U(n,n);for i=n-1: x(i)=(y(i)-U(i,i+1
4、:n)*x(i+1:n)/U(i,i); A=1 2 3;2 5 2 ;3 1 5;b=14 18 20 L,U,x=doolittle1(A,b)L = 1 0 0 2 1 0 3 -8 1U = 1 2 3 0 1 -4 0 0 -36 2.8333 1.33332.8333 平方根法:function L,x=choesky3(A,b)L=zeros(n);L(:,1)=A(:,1)/sqrt(A(1,1); L(k,k)=A(k,k)-L(k,1:k-1)*L(k,1:k-1) L(k,k)=sqrt(L(k,k); for i=k+1: L(i,k)=(A(i,k)-L(i,1:)/
5、L(k,k); y=zeros(n,1);y(1)=b(1)/L(1,1); y(i)=(b(i)-L(i,1:i-1)/L(i,i);x(n)=y(n)/L(n,n); x(i)=(y(i)-L(i+1:n,i)*x(i+1:n)/L(i,i); A=4 -1 1;-1 4.25 2.75;1 2.75 3.5 4.0000 -1.0000 1.0000 -1.0000 4.2500 2.7500 1.0000 2.7500 3.5000 b=4 6 7.25 4.0000 6.0000 7.2500L,x=choesky3(A,b) 2.0000 0 0 -0.5000 2.0000 0 0.5000 1.5000 1.0000
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