Matlab(二分法、简单迭代法、牛顿迭代法、弦截法)&&(高斯消去法、矩阵的三角分解法、雅可比迭代法、高斯-赛德尔迭代法)

function root= Secant( f,a,b,eps )
if(nargin==3)
    eps=1.0e-4;
end
f1=subs(sym(f),findsym(sym(f)),a);
f2=subs(sym(f),findsym(sym(f)),b);
if(f1==0)
    root=a;
end
if(f2==0)
    root=b;
end
if(f1*f2>0)
    disp('两端点乘积大于零');
    return;
else
    tol=1;
    fa=subs(sym(f),findsym(sym(f)),a);
    fb=subs(sym(f),findsym(sym(f)),b);
    root=a-(b-a)*fa/(fb-fa);
    while(tol>eps)
        r1=root;
        fx=subs(sym(f),findsym(sym(f)),r1);
        s=fx*fa;
        if(s==0)
            root=r1;
        else
            if(s>0)
                root=b-(r1-b)*fb/(fx-fb);
            else
                root=a-(r1-a)*fa/(fx-fa);
            end
        end
        tol=abs(root-r1);
    end
end
        

end

------------------------------------------------------
function [ p1,err,k,y ] = Newtonroot1( f,df,p0,eps,maxl )
p0,feval('f',p0)
for k=1:maxl
    p1=p0-feval('f',p0)/feval('df',p0);
    err=abs(p1-p0);
    p0=p1;
    p1,err,k,y=feval('f',p1)
    if(err<eps)|(y==0)
        break;
    end

end

------------------------------------------------------------
function [ p0,k,err,p ] = Fixpt( g,p0,tol,maxl )
P(1)=p0;
for k=2:maxl    
P(k)=feval('g',P(k-1));
k,err=abs(P(k)-P(k-1))
p=P(k);
if(err<tol)
    break;
end;
if(k==maxl)
    disp('over');
end


end
P

function  root  = HalfInterval( f,a,b,eps )
if(nargin==3)
    eps=1.0e-4;
end
f1=subs(sym(f),findsym(sym(f)),a);
f2=subs(sym(f),findsym(sym(f)),b);
if(f1==0)
    root=a;
end
if(f2==0)
    root=b;
end
if(f1*f2>0)
    disp('两端点函数值乘积大于0！');
    return;
else
    root=FindRoots(f,a,b,eps);
end
  
                    
               

end
 
function r=FindRoots(f,a,b,eps)
        f3=subs(sym(f),findsym(sym(f)),a);
         f4=subs(sym(f),findsym(sym(f)),b);
        mf=subs(sym(f),findsym(sym(f)),(a+b)/2);
        if(f3*mf>0)
            t=(a+b)/2;
            r=FindRoots(f,t,b,eps);
        else
            if(f3*mf==0)
                r=(a+b)/2;
            else
                if(abs(b-a)<=eps)
                    r=(b+3*a)/4;
                else
                    s=(a+b)/2;
                    r=FindRoots(f,a,s,eps);
                end
            end
        end
-----------------------------------------------------------------
       function [ x,det,flag ] = Guass( A,b )
%UNTITLED3 Summary of this function goes here
%   Detailed explanation goes here
[n,m]=size(A);
nb=length(b);
if(n~=m)
    error('the rows and columns of matrix A must equal');
    return;
end
if(m~=nb)
    error('the rows and columns of  A must equal b');
    return;
end
flag='OK';
det=1;
x=zeros(n,1);
for(k=1:n-1)
    max1=0;
    for(i=k:n)
    if(abs(A(i,k))>max1)
        max1=abs(A(i,k));
        r=i;
    end
   end
if(max1<1e-10)
    flag='failure';
    return;
end
if(r>k)
    for(j=k:n)
        z=A(k,j);
        A(k,j)=A(r,j);
        A(r,j)=z;
    end
    z=b(k);
    b(k)=b(r);
    b(r)=z;
    det=-det;
end
for(i=k+1:n)
    m=A(i,k)/A(k,k);
    for(j=k+1:n)
        A(i,j)=A(i,j)-m*A(k,j);
    end
    b(i)=b(i)-m*b(k);
end
det=det*A(k,k);
end
det=det*A(n,n);
if(abs(A(n,n))<1e-10)
    flag='failure';
    return;
end
for(k=n:-1:1)
    for(j=k+1:n)
        b(k)=b(k)-A(k,j)*x(j);
    end
    x(k)=b(k)/A(k,k);
end
x(k)=b(k)/A(k,k);
end

--------------------------------------
function [ L,U,flag ] = LU_Demo( A )
%UNTITLED Summary of this function goes here
%   Detailed explanation goes here
[n,m]=size(A);
if(n~=m)
return;
end
L=eye(n);
U=zeros(n);
flag='ok';
for(k=1:n)
    for(j=k:n)
        z=0;
        for(q=1:k-1)
            z=z+L(k,q)*U(q,j);
        end
        U(k,j)=A(k,j)-z;
    end
    if(abs(U(k,k))<eps)
        flag='f';
        return;
    end
    for(i=k+1:k-1)
        z=0;
        for(q=1:k-1)
            z=z+L(i,q)*U(q,k);
        end
        L(i,k)=(A(i,k)-z)/U(k,k);
    end
    
end
-----------------------------------------------------------
function [ x,n ] = Jacobi( A,b,x0,eps,varargin )
%UNTITLED3 Summary of this function goes here
%   Detailed explanation goes here
if(nargin==3)
    eps=1.0e-6;
    M=200;
elseif(nargin<3)
    error
    return
elseif(nargin==5)
    M=varargin{1};
end
D=diag(diag(A));
L=-tril(A,-1);
U=-triu(A,1);
B=D\(L+U);
f=D\b;
x=B*x0+f;
n=1;
while(norm(x-x0)>=eps)
    x0=x;
    x=B*x0+f;
    n=n+1;
if(n>=M)
    disp('duo');
    return;
end
end

-----------------------------------------------
function [ x,n ] = GaussSeidel( A,b,x0,eps,M )
%UNTITLED4 Summary of this function goes here
%   Detailed explanation goes here
if(nargin==3)
    eps=1.0e-6;
    M=200;
elseif(nargin==4)
    M=200;
elseif(nargin<3)
    error;
    return;
end
D=diag(diag(A));
L=-tril(A,-1);
U=-triu(A,1);
G=(D-L)\U;
f=(D-L)\b;
x=G*x0+f;
n=1;
while(norm(x-x0)>=eps)
    x0=x;
    x=G*x0+f;
    n=n+1;
if(n>=M)
    disp('duo');
    return;
end
end