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 $$p(x)=x^2-4x+4$$.

p = [1 -4 4];

Intermediate terms of the polynomial that have a coefficient of0must also be entered into the vector, since the0acts as a placeholder for that particular power ofx.

Create a vector to represent the polynomial $$p(x)=4x^5-3x^2+2x+33$$.

p = [4 0 0 -3 2 33];

Evaluating Polynomials

After entering the polynomial into MATLAB® as a vector, use thepolyval计算多项式在一个特定的函数value.

Usepolyvalto evaluate $$p(2)$$.

polyval(p,2)

ans = 153

Alternatively, you can evaluate a polynomial in a matrix sense usingpolyvalm. The polynomial expression in one variable, $$p(x)=4x^5-3x^2+2x+33$$, becomes the matrix expression

whereXis a square matrix andIis the identity matrix.

Create a square matrix,X, and evaluatepatX.

X = [2 4 5; -1 0 3; 7 1 5]; Y = polyvalm(p,X)

Y =3×3154392 78561 193065 49001 24104 59692 215378 111419 269614