Data: Polynomial Curve Fit

Data: Curve Fit

General data fitting is typically done using polynomials (also in Polynomials). The problem can be specified as

Given a set of x - y data find the best polynomial of given order that will best match the data

For a polynomial of order n, this is an n+1 variable problem. The problem is an example of unconstrained optimization. In numerical analysis course this can be shown to be a linear matrix solution involving the Vandermonde matrix. In addition MATLAB provides a statistical evaluation that provides information on the quality of the fit

In this example

The original data is drawn using the MATLAB code below
The curve is fitted using the Basic Fitting Selection Box from the Tools menu
The data statistics is obtained and printed on the figure using the Data Statistics Selection Box from the Tools menu

MATLAB Code

% Data Analysis - Polynomial Curve fit
% Dr. P.venkataraman
% ---------------------create sample data
x = linspace(0,3,31);
y = 3*exp(-0.5*x).*sin(2*x);
n = 4;    % order of data
%-------------------------------------
format compact
% formatting figure-------------------
set(gcf,'Name','Polynomial Fit', ...
    'NumberTitle','off','Position',[10,350,400,350], ...
    'Color',[0.5 0.8 0.5]);
%-----------------------------------
plot(x,y,'ro','MarkerFaceColor','y', ...
    'MarkerSize',4,'MarkerEdgeColor','k')
% formatting figure-----------
title('\bf\itPolynomial fit','Color','k', ...
    'VerticalAlignment','middle')
ylabel('y', ...
    'FontWeight','b','Color','k', ...
    'VerticalAlignment','bottom');
xlabel('x', ...
    'FontWeight','b','Color','k', ...
    'VerticalAlignment','top');
grid
%---------------------------------