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Applying approximate LU-factorizations as preconditioners in eight iterative methods for solving systems of linear algebraic equations

Zahari Zlatev, Krassimir Georgiev (2013)

Open Mathematics

Many problems arising in different fields of science and engineering can be reduced, by applying some appropriate discretization, either to a system of linear algebraic equations or to a sequence of such systems. The solution of a system of linear algebraic equations is very often the most time-consuming part of the computational process during the treatment of the original problem, because these systems can be very large (containing up to many millions of equations). It is, therefore, important...

Avoiding look-ahead in the Lanczos method and Padé approximation

E. Ayachour (1999)

Applicationes Mathematicae

In the non-normal case, it is possible to use various look-ahead strategies for computing the elements of a family of regular orthogonal polynomials. These strategies consist in jumping over non-existing and singular orthogonal polynomials by solving triangular linear systems. We show how to avoid them by using a new method called ALA (Avoiding Look-Ahead), for which we give three principal implementations. The application of ALA to Padé approximation, extrapolation methods and Lanczos method for...

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