MATLAB Functions | Help Desk |
roots
Polynomial roots
r = roots(c)
r = roots(c)
returns a column vector whose elements are the roots of the polynomial c
.
Row vector c
contains the coefficients of a polynomial, ordered in descending powers. If c
has n+1
components, the polynomial it represents is p = poly(r)
, which returns a row vector whose elements are the coefficients of the polynomial. For vectors, roots
and poly
are inverse functions of each other, up to ordering, scaling, and roundoff error.
The polynomial
is represented in MATLAB as
p = [1 -6 -72 -27]
The roots of this polynomial are returned in a column vector by
r = roots(p) r = 12.1229 -5.7345 -0.3884The algorithm simply involves computing the eigenvalues of the companion matrix:
A = diag(ones(n-2,1),-1); A(1,:) = -c(2:n-1)./c(1); eig(A)It is possible to prove that the results produced are the exact eigenvalues of a matrix within roundoff error of the companion matrix
A
, but this does not mean that they are the exact roots of a polynomial with coefficients within roundoff error of those in c
.
fzero
Zero of a function of one variable
poly
Polynomial with specified roots
residue
Convert between partial fraction expansion and polynomial coefficients