Interpolation and Curve Fitting - Numerical Methods in Engineering with MATLAB - page 121

EXAMPLE 3.7
Write aprogram that interpolates between givendatapoints with the naturalcubic
spline. The programmust be able to evaluate the interpolantformorethan one value
of x .As a test, use datapoints specified in Example 3.4 and compute the interpolant
at x = 1 . 5 and x = 4 . 5 (duetosymmetry, these values shouldbeequal).

Solution The program belowprompts for x ;it isterminatedbypressing the “return”
key.

% Example 3.7 (Cubic spline)
xData = [1; 2; 3; 4; 5];
yData = [0; 1; 0; 1; 0];
k = splineCurv(xData,yData);
while 1
x = input('x = ');
if isempty(x)
fprintf('Done'); break

end
y = splineEval(xData,yData,k,x)
fprintf('\n')

end

Running the program produces the following results:

x=1.5
y=

0.7679

x=4.5
y=

0.7679

x=
Done

PROBLEM SET 3.1

1. Given the datapoints

x − 1 . 2 0 . 3 1 . 1

y − 5 . 76 − 5 . 61 − 3 . 69

determine y at x = 0 using (a)Neville's method and (b) Lagrange's method.