Systems of linear algebraic equations arise in many applications that involve scientific computations, such as signal processing, computational fluid dynamics, and others. Such systems occur naturally or are the result of approximating differential equations by algebraic equations.
Whatever the application, it is always necessary to find an accurate solution for the system of equations in a very efficient way. In matrix-vector notation, such a system of linear algebraic equations has the following form.
where A is an n × n matrix, B is a given vector consisting of n elements, and x is the unknown solution vector to be determined.