Numerical Methods نس ...

Introduction. In this chapter, we will explore direct methods for solving linear systems of equations. These methods aim to provide exact solutions (up to the precision of the computer's arithmetic) by performing a finite sequence of operations on the system's matrix and right-hand side. We will begin by discussing the efficient solution of triangular systems, which serve as building blocks for many direct methods. Next, we will delve into the Gaussian elimination method, a fundamental algorithm for solving general linear systems. Finally, we will interpret Gaussian elimination from a matrix factorization perspective, leading to the concept of LU factorization, which is a powerful tool for solving linear systems and other matrix computations.