Conjugate Gradient Method
The Conjugate Gradient Method is an iterative numerical algorithm for solving systems of linear equations with symmetric, positive-definite matrices, commonly used in optimization and computational science. It efficiently finds solutions by minimizing a quadratic function through conjugate directions, avoiding redundant steps to converge faster than basic gradient descent. It is particularly valuable for large-scale problems where direct methods like Gaussian elimination are computationally prohibitive.
Developers should learn this method when working on optimization problems in machine learning, physics simulations, or engineering applications that involve large sparse matrices, as it reduces memory usage and computation time compared to direct solvers. It is essential for tasks like solving partial differential equations, training support vector machines, or implementing numerical methods in scientific computing, where efficiency and scalability are critical.