Gaussian elimination for the solution of linear systems of equations

Publisher Summary This chapter discusses Gaussian elimination for the solution of linear systems of equations. It focuses on the problem of obtaining the numerical solution of a linear system on a computer. There are two main classes of algorithms to obtain a solution to equation illustrated in the chapter: iterative methods and direct methods. Iterative methods define a sequence of approximations that are expected to be closer and closer to the true solution in some given norm, stopping the iterations by using some predefined criterion and obtaining a vector that is only an approximation of the solution. Direct methods try to compute the solution doing some combinations and modifications of the equations and after a finite number of floating point operations. As computer floating point operations are only done with a certain precision, the computed solution is generally different from the exact solution even with a direct method. The most used direct methods for general matrices belong to a class collectively known as “Gaussian elimination.”