MATLAB: Interesting question: construct a polynomial and then evaluate it

degreepolynomialroot

In the normal polynomial root-finding, we could utilized the roots(x) function and passed a vector a x for root.

But what if we have some function:

where r is some fixed constant.

In such case, the roots function definitely could not used in this case, how can i supposed to construct such function and then find its root?

Thanks for your assistance.

Best Answer

Certainly roots() could be used.

t = a(:) .';
t(r, end) = 0;
t(end-r+1:end) = [];
coeff = fliplr( t );
sols = roots(coeff);

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MATLAB: Using roots with vectorization of a polynomial vs. the function it’s self

Look at what the roots function is documented to do.

r = roots(p) returns the roots of the polynomial represented by p as a column vector. Input p is a vector containing n+1 polynomial coefficients, starting with the coefficient of xn.

It does not accept a vector of values of your function and find the zeros of the function that takes those values. In other words, since x has 201 elements so does y and so r is the roots of a 200th degree polynomial not the 5th degree polynomial you evaluated to compute y. Zero crossings in a vector is better done by comparing the sign of the elements in that vector, or perhaps interpolation and fzero.

On the other hand, y1 does not represent the polynomial you evaluated to compute y. You're missing the constant term, which has to be present in the coefficient vector even if it's 0. But it's closer.

MATLAB: How to write polynomial code

syms x
p(x)=x^2+2*x-3;%as an example
Coeff=coeffs(p(x))';
Coeff=wrev(Coeff);
Roots=roots(Coeff);%roots
Degree=length(Coeff)-1;%degrees
disp(p^3)%calculates p^3
x=0:0.1:1;
plot(x,p(x));grid on;%plots

Best Answer

Related Solutions

MATLAB: Using roots with vectorization of a polynomial vs. the function it’s self

MATLAB: How to write polynomial code

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