Matlab programming code for comparing linear equation and cholesky decomposition method

Please how do I write Matlab programming code for comparing linear equation and cholesky decomposition method

Answer 1

[Kautuk Raj]

To compare solving a linear system using the standard linear equation method and the Cholesky decomposition method in MATLAB, we can write a code that solves a linear system using both methods and compares their execution times. To cite an example:

% Set the size of the matrix
n = 1000;
% Generate a random symmetric positive definite matrix
A = rand(n);
A = A*A';
% Generate a random right-hand side vector
b = rand(n, 1);
% Solve the linear system using the standard method
tic;
x1 = A \ b;
t1 = toc;
% Solve the linear system using the Cholesky decomposition method
tic;
L = chol(A, 'lower');
y = L \ b;
x2 = L' \ y;
t2 = toc;
% Compare the execution times
fprintf('Standard method: %f seconds\n', t1);
fprintf('Cholesky method: %f seconds\n', t2);
fprintf('Speedup factor: %f\n', t1/t2);
% Check the accuracy of the solutions
fprintf('Maximum absolute error: %e\n', max(abs(x1 - x2)));

The results on my machine are:

Standard method: 0.016538 seconds

Cholesky method: 0.007362 seconds

Speedup factor: 2.246400

Maximum absolute error: 3.112644e-07