Numerical Methods for Solving Large Sparse Linear Systems

Abstract

Often used in engineering, scientific computing, and optimization, the study investigates numerical approaches for managing big sparse linear systems. Regarding memory Many of whose entries are zeros, sparse matrices will benefit greatly in large systems using both computational speed and use. Resolving such systems, however, creates difficulties in memory usage and computational complexity, and numerical stability. The essay contrasts direct and iterative methods along with their respective advantages and disadvantages. Direct techniques such LU decomposition yield right results, for larger systems, however, they are rather hard. Iterative methods such as the Conjugate Gradient (CG) method become useful for badly conditioned system (when combined with preconditioning), and can be very beneficial when convergence is accelerated. This article describes the method of solving large sparse linear systems that exist in the real-world using parallelization and preconditioning in combination with iterative methods.