Lanczos Methods in Economics

Abstract

Techniques for solving systems of linear equations are important problems in themselves and they answer basic questions in Numerical Analysis. Moreover, the methods used for linear problems often help to solve non-linear problems, and many iterative schemes for linear systems have led to the development of non-linear iterative methods. The associated difficulties with the numerical resolution of linear systems (instability, ill-conditioning, etc) are the same as those of the more general problems. In Economics, large sparse systems occur frequently, and so the appropriate special methods which are as efficient and reliable as possible should be used. In this paper, we present Lanczos' iterative method and some modifications of it in the context of some problems from economics, where it is undoubtedly a more efficient alternative to the classical methods previously used.