数值计算方法matlab程序

二分法function x0,k=bisect1(fun1,a,b,ep)if nargin0x0=fa,fb;k=0;return;endk=1;while abs(b-a)/2epx=(a+b)/2;fx=feval(fun1,x);if fx*fa 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)if nargin4N=500;endif narginep & k fun1=inline(x+1)(1/3); x0,k=iterate1(fun1,1.5)x0 =1.3247k =7 fun1=inline(x3-1); x0,k=iterate1(fun1,1.5)x0 =Infk =9Steffesen加速迭代（简单迭代法的加速）function x0,k=steffesen1(fun1,x0,ep,N)if nargin4N=500;endif narginep & k fun1=inline(x+1)(1/3); x0,k=steffesen1(fun1,1.5)x0 =1.3247k =3 fun1=inline(x3-1); x0,k=steffesen1(fun1,1.5)x0 =1.3247k =6Newton迭代function x0,k=Newton7(fname,dfname,x0,ep,N)if nargin5N=500;endif narginep & k fname=inline(x-cos(x); dfname=inline(1+sin(x); x0,k=Newton7(fname,dfname,pi/4,1e-8)x0 =0.7391k =4非线性方程求根的Matlab函数调用举例：1.求多项式的根： 求f(x)=x3-x-1=0的根： roots(1 0 -1 -1)ans =1.3247-0.6624 + 0.5623i-0.6624 - 0.5623i2.求一般函数的根 fun=inline(x*sin(x2-x-1),x)fun = Inline function: fun(x) = x*sin(x2-x-1) fplot(fun,-2 0.1);grid on x=fzero(fun,-2,-1)x = -1.5956 x=fzero(fun,-1 -0.1)x = -0.6180x,f,h=fsolve(fun,-1.6)x = -1.5956f = 1.4909e-009h = 1（h0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 -4.0000x = -13 8 2列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n=length(b);A=A,b;for k=1:n-1 %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; end %消元 A(k+1):n,(k+1):(n+1)=A(k+1):n,(k+1):(n+1)-A(k+1):n,k)/A(k,k)*A(k,(k+1):(n+1); A(k+1):n,k)=zeros(n-k,1); end%回代 x=zeros(n,1); x(n)=A(n,n+1)/A(n,n); for k=n-1:-1:1 x(k)=(A(k,n+1)-A(k,(k+1):n)*x(sk+1:n)/A(k,k);end A=2 3 4;3 5 2;4 3 30; b=6,5,32; A,x=gauss5(A,b)A = 4.0000 3.0000 30.0000 32.0000 0 2.7500 -20.5000 -19.0000 0 0 0.1818 0.3636x = -13 8 2三角分解法：Doolittle 分解function 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)*U(1:k-1,n)/U(k,k);Endy=zeros(n,1);x=y;y(1)=b(1);for i=2:n y(i)=b(i)-L(i,1:i-1)*y(1:i-1);endx(n)=y(n)/U(n,n);for i=n-1:-1:1 x(i)=(y(i)-U(i,i+1:n)*x(i+1:n)/U(i,i);end 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 -36x = 2.8333 1.33332.8333 平方根法：function L,x=choesky3(A,b)n=length(A);L=zeros(n);L(:,1)=A(:,1)/sqrt(A(1,1);for k=2:n 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:n L(i,k)=(A(i,k)-L(i,1:k-1)*L(k,1:k-1)/L(k,k); endend y=zeros(n,1);x=y;y(1)=b(1)/L(1,1);for i=2:n y(i)=(b(i)-L(i,1:i-1)*y(1:i-1)/L(i,i);endx(n)=y(n)/L(n,n);for i=n-1:-1:1 x(i)=(y(i)-L(i+1:n,i)*x(i+1:n)/L(i,i);end A=4 -1 1;-1 4.25 2.75;1 2.75 3.5A = 4.0000 -1.0000 1.0000 -1.0000 4.2500 2.7500 1.0000 2.7500 3.5000 b=4 6 7.25b = 4.0000 6.0000 7.2500L,x=choesky3(A,b)L = 2.0000 0 0 -0.5000 2.0000 0 0.5000 1.5000 1.0000x = 1 1 1迭代法求方程组的解Jacobi迭代法：function x,k=jacobi2(a,b,x0,ep,N)%本算法用Jacobi迭代求解ax=b,用分量形式n=length(b);k=0;if nargin5 N=500;endif nargin4 ep=1e-5;endif narginep & kN k=k+1; x0=x; for i=1:n y(i)=b(i); for j=1:n if j=i y(i)=y(i)-a(i,j)*x0(j); end end if abs(a(i,i)1e-10|k=N warning(a(i,i) is too small); return end y(i)=y(i)/a(i,i); end x=y; enda=4 3 0;3 4 -1; 0 -1 4;b=24 30 -24；x,k=jacobi2(a,b)x = 3.0000 4.0000 -5.0000k =59Gauss-seidel迭代法：function x,k=gaussseide2(a,b,x0,ep,N)%本算法用Gauss-seidel迭代求解ax=b,用分量形式n=length(b);k=0;if nargin5 N=500;endif nargin4 ep=1e-5;endif narginep & kN k=k+1; x0=x; y=x; for i=1:n z(i)=b(i); for j=1:n if j=i z(i)=z(i)-a(i,j)*x(j); end end if abs(a(i,i)1e-10|k=N warning(a(i,i) is too small); return end z(i)=z(i)/a(i,i); x(i)=z(i); end endx,k=gaussseide2(a,b)x = 3.0000 4.0000 -5.0000k = 25最速下降法function x,k=zuisuxiajiang(A,b,x0,ep,N)%本算法用最速下降算法求解正定方程组Ax=b,n=length(b);if nargin5 N=500;endif nargin4 ep=1e-8;endif narginep & kN k=k+1; x0=x;lamda=(d*d)/(d*A*d);x=x0+lamda*d;r=b-A*x;d=r;endif k=N warning(已达最大迭代次数)end共轭梯度算法function x,k=gongertidufa(A,b,x0,ep,N)%本算法用共轭梯度算法求解正定方程组Ax=b,n=length(b);if nargin5 N=500;endif nargin4 ep=