MATLAB: Function of roots

function

I have another problem it says:

give the function whose roots are 4, -3, -2, 1/5 and 0.

should I use poly(x) or roots(x)?

Best Answer

roots() is to find the roots of a polynomial that has the given coefficients. The opposite of it is poly.

This is described right in the documentation, http://www.mathworks.com/help/techdoc/ref/poly.html

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MATLAB: How to find the roots of large number of polynomials arranged in matrix array

Hi,

you could use cellfun to apply roots to your Matrix:

% Matrix containing 3 polynomials of order 4 
A = [1 1 -2 2 -3; 2 3 -2 -2 1; 0 0 -4 2 -7]
% Convert to cell array of single polynomials
B =mat2cell(A,ones(1,size(A,1)),size(A,2))
% calculate roots for every polynomial and save in new cell array
C = cellfun(@roots,B,'UniformOutput',0)
% Access the roots of the first polynomial
C{1,:}

Best regards

Stephan

MATLAB: Eigenvalue doesn’t zero the characteristic polynomial

The reason for this is that the characteristic polynomial for matrices of even moderate size tends to be ill-conditioned, no matter the condition number of the matrix. For this reason, numerical methods do not use the characteristic polynomial.

For symbolic numbers, the characteristic polynomial works great, but copy-pasting a number such as 37.721878707889458815773572522044 puts you back in the numeric point of view. If you pass in

 s = solve(polyA);
 double(subs(polyA,s(ind)))

this should return zero for every element of s.

To visualize the problem with using the characteristic polynomial, try plotting it:

 x = linspace(-100, 100);
 y = double(subs(polyA, sym(x)));
 plot(x, y);
 ylim([-1e10, 1e10]) % adjust according to the values you see

You should see a bunch of nearly vertical lines crossing the x-axis: a small change in x will result in y being way off.

Best Answer

Related Solutions

MATLAB: How to find the roots of large number of polynomials arranged in matrix array

MATLAB: Eigenvalue doesn’t zero the characteristic polynomial

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