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%% Create and Evaluate Polynomials % This example shows how to represent a polynomial as a vector in MATLAB(R) % and evaluate the polynomial at points of interest. % Copyright 2015 The MathWorks, Inc. %% Representing Polynomials % MATLAB(R) represents polynomials as row vectors containing coefficients % ordered by descending powers. For example, the three-element vector % % p = [p2 p1 p0]; % % represents the polynomial % % $$p(x) = p_2x^2+p_1x+p_0.$$ % %% % 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 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 $p(x)=4x^5-3x^2+2x+33$. p = [4 0 0 -3 2 33]; %% Evaluating Polynomials % After entering the polynomial into MATLAB(R) as a vector, use the % |polyval| function to evaluate the polynomial at a specific value. % % Use |polyval| to evaluate $p(2)$. polyval(p,2) %% % Alternatively, you can evaluate a polynomial in a matrix sense using % |polyvalm|. The polynomial expression in one variable, % $p(x)=4x^5-3x^2+2x+33$, becomes the matrix expression % % $$p(X)=4X^5-3X^2+2X+33I,$$ % % 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)