ABSTRACT
This chapter discusses linear systems and more specialized methods to efficiently handle large linear systems. It explores ill-conditioning symptoms, as well as pertinent remedies. The chapter provides iterative solution of nonlinear systems of equations. Numerical methods for solving linear systems of equations are divided into two categories: direct methods and indirect methods. Gauss elimination is a procedure that transforms a linear system of equations into upper-triangular form, the solution of which is found by back substitution. There are other direct methods that require fewer operations than Gauss elimination. These methods make use of the LU factorization of the coefficient matrix. The chapter also provides the conditioning of a linear system and how it may impact the error associated with a computed solution. Systems of nonlinear equations can be solved numerically by either using Newton's method or the fixed-point iteration method.
