Finding real roots of cubic polynomial

Question

S. R. S. 2020-11-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/651298-finding-real-roots-of-cubic-polynomial

评论： S. R. S. 2020-11-18

I want to find the only one real roots of the equation and wrote the following code:

e = 0.3; gama = 0.8; damp = 0.0031; A = 12; M = 2*10^-4; mu = 0.05/M; St = 0.2; %parameters
Ur = 4:0.1:6;
for i = 1:size(Ur,2)
    del(i) = 1/(St*Ur(i));
    p(i,:)=roots([1   (-(1+2*del(i)^2-(2*damp*del(i)+(gama/mu))^2)+A*M)   (-(-2*del(i)^2+(2*damp*del(i)+(gama/mu))^2-del(i)^4)-A*M*del(i)^2)   (-del(i)^4)]);
    r = p;
    r = r(imag(r) == 0 );
end

Only one real root corresponding to each 'del(i)' is required but in some iteration, 'del(i)' leads to all three real roots of 'p'. (If all the three roots are real, max value of roots out of three would be considered)

How can I improve my code?

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Andrei Bobrov 2020-11-17

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/651298-finding-real-roots-of-cubic-polynomial#answer_547668

在 MATLAB Online 中打开

e = 0.3;
gama = 0.8;
damp = 0.0031;
A = 12;
M = 2*10^-4;
mu = 0.05/M;
St = 0.2;
AM = A*M; 
%parameters
Ur = (4:0.1:6)';
n = numel(Ur);
del = 1./(St*Ur);
del2 = del.^2;
B = 2*del2-(2*damp*del+gama/mu).^2;
X = [ones(n,1) ,  AM-1-B ,  B+del2.^2-AM*del2   ,-del2.^2];
r = zeros(n,1);
for i = 1:n
    p = roots(X(i,:));
    r(i) = max(p(imag(p) == 0 ));
end