When solving a large-scale linear system of the form Ax = b where A is symmetric and positive definite, which specific matrix decomposition provides the most computationally efficient solution?

The most computationally efficient method for solving a linear system Ax = b where A is symmetric and positive definite is the Cholesky decomposition. A matrix is symmetric if it is equal to its own transpose, meaning it remains the same when rows and columns are swapped, and it is positive definite if all of its eigenvalues are positive, ensuring it is invertible and stable. The Cholesky de....