Conjugate Gradient Method

The Conjugate Gradient Method is an algorithm used to efficiently solve large systems of linear equations, especially those involving many variables and symmetric, positive-definite matrices. Instead of checking every possible solution, it iteratively refines an estimate by moving in specific directions that are conjugate (independent with respect to the matrix). This approach speeds up convergence, making it computationally attractive in fields like engineering and scientific computing. Essentially, it finds the best solution by smartly navigating the problem space, reducing the effort compared to more straightforward methods.