Question

Design a MATLAB code to construct a natural cubic spline P(x) that passes though the points (1, 1), (4, 1/4), (7, 1/7), (10, 1/10), (13, 1/13) and (16, 1/16). (a) Use the constructed cubic spline to interpolate x = 3; (b) Find the error e_1 = |1/3 - P(3)|;

Answer 1

% Initialize 2 arrays with the given points

% one for x coordinate and one for y coordinate

x = [1, 4, 7, 10, 13, 16];
y = [1, 1.0/4.0, 1.0/7.0, 1.0/10.0, 1.0/13.0, 1.0/16.0];

inter = 3;
% use the predefined spline function in matlab

% a)

% the parameter are the array of x coordinate, the array of y coordinate and the value which we want to interpolate
inValue = spline(x, y, inter);
% b)

%To find the error we use the abs function which gives the absolute value (Positive value) of the variable passed as a parameter.
e1 = abs(1.0/3.0 - inValue);

% Answers-

% a) 0.3931

% b) 0.0597