Abstract
Linear systems arise very frequently in quantitative modeling and are at the core of classical optimization and Least Squares problems. There are two broad classes of methods, direct and iterative ones, for the solution of linear systems. Within these classes there exists a variety of algorithms; the appropriate choice for a given problem depends on the structure and quantification of the coefficient matrix of the linear system to be solved. This chapter explains the main algorithms and provides pseudocode for them, it also presents a classification of the problems and a discussion about what method is most efficient for a given problem. Sparse linear systems are part of the discussion. For several methods Matlab code is provided together with numerical illustrations.
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