Preconditioned Conjugate Gradient
Preconditioned Conjugate Gradient (PCG) is an iterative numerical algorithm for solving large, sparse, symmetric positive-definite systems of linear equations. It enhances the standard Conjugate Gradient method by applying a preconditioner—a matrix that approximates the inverse of the system matrix—to accelerate convergence and improve computational efficiency. This method is widely used in scientific computing, engineering simulations, and machine learning for problems like finite element analysis and optimization.
Developers should learn PCG when working on applications involving large-scale linear systems, such as computational fluid dynamics, structural analysis, or image processing, where direct solvers are too slow or memory-intensive. It is particularly valuable in high-performance computing and simulations requiring fast, iterative solutions with reduced computational cost, making it essential for fields like physics-based modeling and data science.