Create and Evaluate Polynomials
This example shows how to represent a polynomial as a vector in MATLAB® and evaluate the polynomial at points of interest.
Representing Polynomials
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 x
.
Create a vector to represent the polynomial .
p = [4 0 0 -3 2 33];
Evaluating Polynomials
After entering the polynomial into MATLAB® as a vector, use the polyval
function to evaluate the polynomial at a specific value.
Use polyval
to evaluate .
polyval(p,2)
ans = 153
Alternatively, you can evaluate a polynomial in a matrix sense using polyvalm
. The polynomial expression in one variable, , becomes the matrix expression
where X
is a square matrix and I
is the identity matrix.
Create a square matrix, X
, and evaluate p
at X
.
X = [2 4 5; -1 0 3; 7 1 5]; Y = polyvalm(p,X)
Y = 3×3
154392 78561 193065
49001 24104 59692
215378 111419 269614
See Also
polyval
| polyvalm
| poly
| roots