3.4 Numerical Solutions of Linear Systems

The solution of linear systems of equations is a topic that is widely applicable not only in engineering and technology but also in many other fields. There are two main categories of numerical methods for solving linear systems:

  1. Direct methods, where an accurate solution to the system is found through a finite number of arithmetic operations, assuming no rounding errors. Direct methods include matrix division methods and elimination methods.

  2. Iterative methods, where an initial guess for the solution is provided, and successive approximations are made to refine the solution over iterations.