Write a computer program that estimates a f(x) dx by S(x) dx, where S is the natural cubic spline having knots a + ih and interpolating f at these knots. Here 0 ≤ i ≤ n and h = (b-a)/n. First obtain a formula for 10 S(x) dx
Write a computer program that estimates a f(x) dx by S(x) dx, where S is the natural cubic spline having knots a + ih and interpolating f at these knots. Here 0 ≤ i ≤ n and h = (b-a)/n. First obtain a formula for 10 S(x) dx
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I am getting an error in my MATLAB code as shown in the image. I have also attach an image of the problem I am trying to solve in MATLAB. Can you help me fix the error?
Transcribed Image Text:Write a computer program that estimates ſå f(x) dx by f S(x) dx, where S is the natural
cubic spline having knots a + ih and interpolating f at these knots. Here 0 ≤ i ≤ n and
h = (b-a)/n. First obtain a formula for
10
S(x) dx
![clc;
clear all;
% Example usage
a = 0;
b = 1;
n = 10;
f = @(x) x.^2; % Example function: f(x) = x^2
% Generate knots.
h = (ba) / n;
knots = a + (0:n) * h;
% Evaluate function values at knots
f_values = f(knots);
% Calculate natural cubic spline coefficients
spline_coefficients = spline(knots, [0, f_values, 0]);
% Define the spline function
spline_function = @(x) ppval (mkpp (knots, spline_coefficients),
% Define the integral function for the spline using trapezoida
integral_spline = @(x) trapz(x, spline_function(x));
% Calculate the integral using quad function
integral_estimate = integral(integral_spline, 0, 1);
% Display the result
fprintf('Estimated integral: %f\n', integral estimate);
Error using mkpp
The requested number of polynomial pieces, 10, is
incompatible with the proposed size, [1], of a
coefficient
and the number, 1, of scalar coefficients provided.
Error in untitled3 (line 21)
spline_function = @(x) ppval (mkpp (knots, spline_coeffici
Error in untitled3 (line 24)
integral_spline = @(x) trapz(x, spline_function(x));
Error in integralCalc/iterateScalarValued (line 314)
fx = FUN(t);
Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u, tinterval
Error in integralCalc (line 75)
[q,errbnd] vadapt (@AtoBInvTransform, interval);
Error in integral (line 87)
Q-integralCalc(fun, a, b, opstruct);](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad0d55fe-d83b-4711-86a1-cee8ecea510f%2Fe73aa884-7fd8-47af-b07e-8dada1e9ac2d%2Fzind4uc_processed.png&w=3840&q=75)
Transcribed Image Text:clc;
clear all;
% Example usage
a = 0;
b = 1;
n = 10;
f = @(x) x.^2; % Example function: f(x) = x^2
% Generate knots.
h = (ba) / n;
knots = a + (0:n) * h;
% Evaluate function values at knots
f_values = f(knots);
% Calculate natural cubic spline coefficients
spline_coefficients = spline(knots, [0, f_values, 0]);
% Define the spline function
spline_function = @(x) ppval (mkpp (knots, spline_coefficients),
% Define the integral function for the spline using trapezoida
integral_spline = @(x) trapz(x, spline_function(x));
% Calculate the integral using quad function
integral_estimate = integral(integral_spline, 0, 1);
% Display the result
fprintf('Estimated integral: %f\n', integral estimate);
Error using mkpp
The requested number of polynomial pieces, 10, is
incompatible with the proposed size, [1], of a
coefficient
and the number, 1, of scalar coefficients provided.
Error in untitled3 (line 21)
spline_function = @(x) ppval (mkpp (knots, spline_coeffici
Error in untitled3 (line 24)
integral_spline = @(x) trapz(x, spline_function(x));
Error in integralCalc/iterateScalarValued (line 314)
fx = FUN(t);
Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u, tinterval
Error in integralCalc (line 75)
[q,errbnd] vadapt (@AtoBInvTransform, interval);
Error in integral (line 87)
Q-integralCalc(fun, a, b, opstruct);
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