Next: Finding Roots, Up: Polynomial Manipulations
The value of a polynomial represented by the vector c can be evaluated at the point x very easily, as the following example shows.
N = length(c)-1; val = dot( x.^(N:-1:0), c );
While the above example shows how easy it is to compute the value of a
polynomial, it isn't the most stable algorithm. With larger polynomials
you should use more elegant algorithms, such as Horner's Method, which
is exactly what the Octave function polyval
does.
In the case where x is a square matrix, the polynomial given by
c is still well-defined. As when x is a scalar the obvious
implementation is easily expressed in Octave, but also in this case
more elegant algorithms perform better. The polyvalm
function
provides such an algorithm.
Evaluate a polynomial.
polyval (
c,
x)
will evaluate the polynomial at the specified value of x.If x is a vector or matrix, the polynomial is evaluated at each of the elements of x.
See also: polyvalm, poly, roots, conv, deconv, residue, filter, polyderiv, polyinteg.
Evaluate a polynomial in the matrix sense.
polyvalm (
c,
x)
will evaluate the polynomial in the matrix sense, i.e. matrix multiplication is used instead of element by element multiplication as is used in polyval.The argument x must be a square matrix.
See also: polyval, poly, roots, conv, deconv, residue, filter, polyderiv, and polyinteg.