SIAM Journal on Scientific and Statistical Computing
A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms, Part II
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
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Techniques for solving systems of linear equations are important problems which answer basic questions in Numerical Analysis. Moreover, the methods used for linear problems often help 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 more general problems. Large sparse systems frequently occur in economic models and many other applications. Thus, appropriate special methods which are efficient and reliable should be used whenever possible. In this paper, we present Lanczos' iterative method and some modifications to it in the context of solutions to problems using dynamic models. It is clearly a more efficient alternative to the classical methods previously used when solving these problems.