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

概论

对Matlab非线性方程求解的概括



代码演示

Matlab符号法

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))];

fzero



-

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

roots



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

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)

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;

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

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);

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