Conjugate Gradient
The Conjugate Gradient method is an iterative algorithm for solving systems of linear equations, particularly those that are symmetric and positive-definite. It is widely used in numerical linear algebra and optimization, efficiently finding solutions by minimizing the quadratic form associated with the matrix. This method is favored for its convergence properties and low memory requirements compared to direct solvers.
Developers should learn the Conjugate Gradient method when working on problems involving large, sparse linear systems, such as in finite element analysis, computational fluid dynamics, or machine learning optimizations. It is essential for performance-critical applications where direct methods like Gaussian elimination are too slow or memory-intensive, making it a key tool in scientific computing and engineering simulations.