matlab 01---解简单方程 方程组 二分法

1. 解一元方程;

% x^2-4=12,求x;

syms x;
f=x^2-4-12;
solve(f)

2. 解二元一次方程组—inv()

注：对于 Ax=b;
两种解法：
x=inv(A)*b;
x=A\b; 左除

左除\ 右除/
A\B=inv(A) * B 左除
A/B=A * inv(B) 右除

% x + 2*y = 8
% 2*x + 3*y =13

A=[1,2;2,3];
b=[8;13];
x=inv(A)*b
%或 x=A\b

或：

syms x y;
[x y]=solve(x+2*y==8,2*x+3*y==13)

3. 解二元二次方程—solve vpa

vpa(); 函数求解

% x^2 + 3*y + 1=0
% y^2 + 4*x + 1=0

syms x y;
[x y]=solve(x^2+3*y+1==0,y^2+4*x+1==0);
x=vpa(x,4)% 4表示4位有效数字
y=vpa(y,4)
%解得四组解

4. 解一元多次方程—roots()

a4*x^4+a3*x^3+a2*x^2+
root([a4 a3 a2 a1 a0]);………………
%example：x^4+3*x^2-4*x+5=0
rts=roots([1 0 3 -4 5]) %即可得出结果

5. 用二分法解一元高次方程

%解一元高次方程 用二分法 
%仅限于具有实数根的方程
%input:
%a,b:the left and right value of the interval  which the root is in
%f:the function that transform from the equation
%tol:the accuracy of root
%output:
%x:the solution of the equation
%interations:the number of interations which is to solve the equation
clc;
close;
clear;

a=input('请输入根的下限:');%0
b=input('请输入根的上限:');%10
tol=input('请输入根的精度:');%0.1
interations=0;
%f(a)*f(b)<0  只考虑该区间有解的情况
while (b-a)>tol
   m=(a+b)/2;
   if f(m)==0
       break;%此时 m为f(x)的根 跳出while循环 迭代次数为0
   end
   if f(a)*f(m)>0
       a=m;
   else
       b=m;
   end
   interations=interations+1;
end
x=(a+b)/2;
disp(['方程的根为：',num2str(x)]);
disp(['迭代次数为：',num2str(interations)]);

function y0=f(x)
y0=x^2-1.23;
end

6. 解二元一次方程

function x=quadratic(a,b,c)
%equation:a*x^2+b*x+c=0
%input:a,b,c
%output:x=[x1,x2],the two solutions of this equation

if a==0&b==0&c==0
    %disp(' ')  空一行显示
    disp('solution inderminate');%解不确定
elseif a==0&b==0
    disp('there is no solution');
elseif a==0
    disp('only one root:equation is linear');
    disp('   x1             x2');
    x1=-c/b;
    x2=NaN;
    disp([x1 x2]);
elseif b^2<4*a*c
    disp('x1,x2 are complx roots');
    x1=(-b+sqrt(b^2-4*a*c))/(2*a);
    x2=(-b-sqrt(b^2-4*a*c))/(2*a);
    disp('    x1                  x2');
    disp([x1 x2]);
elseif b^2==4*a*c
    x1=-b/(2*a);
    x2=x1;
    disp('equal roots');
    disp('    x1     x2');
    disp([x1 x2]);
else
    x1=(-b+sqrt(b^2-4*a*c))/(2*a);
    x2=(-b-sqrt(b^2-4*a*c))/(2*a);
    disp('    x1           x2');
    disp([x1 x2]);
end
end

%verify
%{
a=0.5;b=2;c=1; 
quadratic(a,b,c)
    x1           x2
   -0.5858   -3.4142
%}