MATLAB Implementation of Cholesky Decomposition Algorithm

In this article, I present my MATLAB implementation of the Cholesky decomposition algorithm. This program efficiently solves matrix factorization problems, particularly valuable in mathematical and engineering applications. The implementation utilizes fundamental mathematical concepts and formulas from linear algebra and matrix theory. Cholesky decomposition is a specialized matrix factorization method that decomposes a symmetric positive-definite matrix into the product of a lower triangular matrix and its transpose. This approach enables faster solutions for linear systems and least squares problems compared to general decomposition methods. The MATLAB code implements the standard Cholesky algorithm using nested loops for matrix traversal and conditional checks for positive-definite verification. Key functions include: - Matrix symmetry validation - Positive-definite condition checking - Lower triangular matrix construction - Efficient memory allocation for large matrices The algorithm proceeds by computing each element of the lower triangular matrix L using the formula: L(i,j) = (A(i,j) - sum(L(i,k)*L(j,k)))/L(j,j) for the diagonal elements, and similar computations for off-diagonal elements. This implementation includes error handling for non-symmetric matrices and matrices that fail the positive-definite test, providing appropriate warning messages. The code also features optimization for computational efficiency and memory management. I hope this program proves useful for your computational needs. If you have any questions or suggestions for improvement, please feel free to contact me.