3

Linear Systems of Equations

In this chapter, we shall study direct and iterative methods to solve linear system of equations. Among the direct methods, we shall study Gauss elimination method and its modification by Jordan, Crout, and triangularization methods. Among the iterative methods, we shall study Jacobi and Gauss–Seidel methods.

3.1 DIRECT METHODS

Matrix Inversion Method

Consider the system of n linear equations in n unknowns:

images

The matrix form of the system (3.1) is

 

AX = B,                 (3.2)

where

Suppose A is non-singular, ...

Get Numerical Methods now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.