This example shows how to represent a polynomial as a vector in MATLAB® and evaluate the polynomial at points of interest.
MATLAB® represents polynomials as row vectors containing coefficients ordered by descending powers. For example, the three-element vector
p = [p2 p1 p0];
represents the polynomial
Create a vector to represent the quadratic polynomial .
p = [1 -4 4];
Intermediate terms of the polynomial that have a coefficient of
0 must also be entered into the vector, since the
0 acts as a placeholder for that particular power of
Create a vector to represent the polynomial .
p = [4 0 0 -3 2 33];
After entering the polynomial into MATLAB® as a vector, use the
polyval function to evaluate the polynomial at a specific value.
polyval to evaluate
ans = 153
Alternatively, you can evaluate a polynomial in a matrix sense using
polyvalm. The polynomial expression in one variable,
, becomes the matrix expression
X is a square matrix and
I is the identity matrix.
Create a square matrix,
X, and evaluate
X = [2 4 5; -1 0 3; 7 1 5]; Y = polyvalm(p,X)
Y = 154392 78561 193065 49001 24104 59692 215378 111419 269614