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hello everyone
I am practicing numerical differentiation. However, the numerical analysis values and actual values do not appear on the graph at the same time and seem to conflict. Where did we go wrong? Thank you for reading this long sentence. have a good day:)
here is my code :
clc; clear all; close all;
fun = @(t) -0.01953125.*t.^2 + 18.75.*t
est_point = 100;
da = 1;
dfda_central = (fun(est_point + da) - fun(est_point - da))./2*da
x = 0:0.01:960;
fx = fun(x);
dfda_true = -0.0390625.*est_point + 18.75
dgraph = @(point, dfda, t) dfda*t + (fun(point) - dfda*point);
figure(1)
plot(x,fx,'black','linewidth',2); hold on;
plot(x, dgraph(est_point, dfda_central, x),'red'); hold on;
plot(x, dfda_true,'blue'); hold on;
grid on;
rel_error=norm(dfda_true-dfda_central)/norm(dfda_true);
disp(rel_error);
disp(dfda_true);
采纳的回答
clc; clear all; close all;
% Define the function
fun = @(t) -0.01953125.*t.^2 + 18.75.*t;
% Estimation point and step size
est_point = 100;
da = 1;
% Central difference calculation
dfda_central = (fun(est_point + da) - fun(est_point - da)) / (2*da);
% Define the range and function values for plotting
x = 0:0.01:960;
fx = fun(x);
% True derivative value
dfda_true = -0.0390625.*est_point + 18.75;
% Define the line representing the central difference derivative
dgraph = @(point, dfda, t) dfda * t + (fun(point) - dfda * point);
% Plot the original function
figure(1);
plot(x, fx, 'black', 'linewidth', 2); hold on;
% Plot the central difference approximation
plot(x, dgraph(est_point, dfda_central, x), 'red');
% Plot the true derivative as a constant line
plot(x, dfda_true * ones(size(x)), 'blue');
% Add grid and legend
grid on;
legend('Function', 'Central Difference Approximation', 'True Derivative');
% Calculate and display the relative error
rel_error = norm(dfda_true - dfda_central) / norm(dfda_true);
disp(['Relative Error: ', num2str(rel_error)]);
disp(['True Derivative: ', num2str(dfda_true)]);
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