第一，二种边界条件的三次样条插值法

资 源 简 介

第一，二种边界条件的三次样条插值法matlab代码

详 情 说 明

In order to perform cubic spline interpolation for the first and second boundary conditions, we can utilize the following Matlab code:

% Define the data points and boundary conditions

x = [x1 x2 x3 ... xn];

y = [y1 y2 y3 ... yn];

y1_prime = ...; % First boundary condition

y2_prime = ...; % Second boundary condition

% Calculate the coefficients for the cubic polynomials between each pair of data points

h = diff(x);

mu = h(1:end-1) ./ (h(1:end-1) + h(2:end));

lambda = 1 - mu;

d = (6 ./ (h(1:end-1) + h(2:end))) .* (diff(y) ./ diff(x));

d = [y1_prime; d; y2_prime];

A = spdiags([lambda(2:end) 2*ones(n-2,1) mu(1:end-1)], [-1 0 1], n-2, n-2);

c = A d(2:end-1);

% Use the coefficients to interpolate between the data points

xx = linspace(min(x),max(x),num_points); % Define the points at which to evaluate the interpolant

yy = zeros(size(xx));

for i = 1:length(xx)

j = find(x <= xx(i), 1, 'last');

if j == n

j = j - 1;

end

h_j = x(j+1) - x(j);

yy(i) = ((x(j+1)-xx(i))^3*c(j) + (xx(i)-x(j))^3*c(j+1)) / (6*h_j) + ...

((y(j)/h_j - h_j*c(j)/6)*(x(j+1)-xx(i)) + (y(j+1)/h_j - h_j*c(j+1)/6)*(xx(i)-x(j)));

end

This code will allow you to perform cubic spline interpolation with ease, providing accurate and smooth results for your data.