r = roots(p)
c
has n+1
components, the polynomial it represents is
If c
is a row vector containing the coefficients of a polynomial, roots(c)
is a column vector whose elements are the roots of the polynomial.
If r
is a column vector containing the roots of a polynomial, poly(r)
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.
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
-0.3884
It is possible to prove that the results produced are the exact eigenvalues of a matrix within roundoff error of the companion matrixA = diag(ones(n-1,1)),-1);
A(1,:) = -c(2:n-1)/c(1);
eig(A)
A
, but this does not mean that they are the exact roots of a polynomial with coefficients within roundoff error of those in c
.
conv
,fzero
,poly
,polyval
,residue
(c) Copyright 1994 by The MathWorks, Inc.