Matlab非线性方程求解

Matlab求解

• 非线性方程求解

最近准备数学竞赛需要对Matlab重新进行一个系统的学习，于是将在学习中学到的东西以博客的形式记录一下，这里介绍的是Matlab中的非线性方程求解

1. 概论

   对Matlab非线性方程求解的概括

   

2. 代码演示

   1. Matlab符号法

      1. fsolve

         

         -x0 = [-5;-5];

         options = optimset('Display','iter');

         [x,fval] = fsolve(@myfunction,x0,options);

         %function F = myfunction(x)

         %F = [2*x(1)-x(2)-exp(-x(1));-x(1)+2*x(2)-exp(-x(2))];

      2. fzero

         

         -x = fzero('x^4+5*x^2+3*x-20',-2);

      3. roots

         

         -[x] = roots([1 0 5 3 -20]);

      4. solve

         

         -%方程组

         a = 'x^2 + sqrt(5)*x = -1';

         b = 'x + 3*z^2 = 4';

         c = 'y*z + 1 = 0';

         [u,v,w] = solve(a,b,c);

         vpa(u,6)

         vpa(v,6)

         vpa(w,6)

         %方程

         [x] = solve('x^3-x-1=0');

         vpa(x,6)

   2. Newton法

      

      -newton('f','df',1.2,10^(-6),10)

      这里的newton算法：

      -function [p1,err,k,y] = newton(f,df,p0,delta,max1)

      p0,feval(f,p0)

      for k = 1:max1

      p1 = p0 - feval(f,p0)/feval(df,p0);

      err = abs(p1 - p0);

      p0 = p1;

      p1,err,k,y = feval(f,p1)

      if(err<delta)|(y == 0)

      break

      end

      p1,err,k,y = feval(f,p1)

      end

      f函数：

      -function y = f(x)

      y = x^3 - 3*x + 2;

      df函数：

      -function y = df(x)

      y = 3*x^2 - 3;

   3. 迭代法

      迭代算法：

      -function [p0,k,err,p] = fixpt(g,p0,tol,max1)

      P(1) = p0;

      for k = 2:max1

      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 == max1

      disp('maximum number of iteration exceeded');

      end

      end

      P

   4. 二分法

      

      二分算法：

      -function [c,err,yc] = bisect(f,a,b,delta)

      if nargin < 4 delta = 1e-10;end

      ya = feval(f,a);

      yb = feval(f,b);

      if yb == 0

      c = b;

      return

      end

      if ya*yb>0

      disp('(a,b)不是有根区间');

      return

      end

      max1 = 1 + round((log(b-a)-log(delta))/log(2));

      for k = 1:max1

      c = (a+b)/2;

      yc = feval(f,c);

      if yc == 0

      a = c;

      b = c;

      break;

      elseif yb*yc > 0

      b = c;

      yb = yc;

      else

      a = c;

      ya = c;

      end

      if(b-a) < delta

      break

      end

      end

      k = (a+b)/2;

      c = (a+b)/2;

      err = abs(b-a);

      yc = feval(f,c);

   5. 弦位法

      

      弦位算法：

      -function [p1,err,k,y] = secant(f,p0,p1,delta,max1)

      p0,p1,feval(f,p0),feval(f,p1),k=0,

      for k = 1:max1

      p2 = p1 - feval(f,p1)*(p1-p0)/(feval(f,p1)-feval(f,p0));

      err = abs(p2 - p1);

      p0 = p1;

      p1 = p2;

      p1,err,k,y=feval(f,p1)

      if(err < delta) | (y == 0)

      break

      end

      end

代码下载地址：http://download.csdn.net/detail/qq_34861102/9922160

原文地址：http://blog.csdn.net/qq_34861102/article/details/76724026