Metode Kaczmarz untuk menyelesaikan sistem persamaan linear

Abstract

A system of linear equations is often involved in science and engineering problems. There are many methods available for solving system of linear equations, both analytically and numerically. Kaczmarz method is one of iterative methods for solving such system. Orthogonal projections are used in this method. The sequence of approximate solutions generated by algorithm for this method is convergent for an arbitrary initial solution. A proof of the convergence is given. If the system of linear equations is consistent, then the sequence of approximate solutions converges to the exact solution. This shows that Kaczmarz method is a good method. Implementation of this method is done using MATLAB R2008b. Some systems of linear equations are generated, and then solved numerically using the program. The results show that the more iteration used in the solution approximation, the smaller norm of residual obtained.