www.gusucode.com > matlab 案例源码 matlab代码程序 > matlab/CreateAndEvaluatePolynomialsExample.m

    %% 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)