Displaying similar documents to “Using successive approximations for improving the convergence of GMRES method”

Inversion of square matrices in processors with limited calculation abillities

Krzysztof Janiszowski (2003)

International Journal of Applied Mathematics and Computer Science

Similarity:

An iterative inversion algorithm for a class of square matrices is derived and tested. The inverted matrix can be defined over both real and complex fields. This algorithm is based only on the operations of addition and multiplication. The numerics of the algorithm can cope with a short number representation and therefore can be very useful in the case of processors with limited possibilities, like different neuro-computers and accelerator cards. The quality of inversion can be traced...

New SOR-like methods for solving the Sylvester equation

Jakub Kierzkowski (2015)

Open Mathematics

Similarity:

We present new iterative methods for solving the Sylvester equation belonging to the class of SOR-like methods, based on the SOR (Successive Over-Relaxation) method for solving linear systems. We discuss convergence characteristics of the methods. Numerical experimentation results are included, illustrating the theoretical results and some other noteworthy properties of the Methods.

A one parameter method for the matrix inverse square root

Slobodan Lakić (1997)

Applications of Mathematics

Similarity:

This paper is motivated by the paper [3], where an iterative method for the computation of a matrix inverse square root was considered. We suggest a generalization of the method in [3]. We give some sufficient conditions for the convergence of this method, and its numerical stabillity property is investigated. Numerical examples showing that sometimes our generalization converges faster than the methods in [3] are presented.

Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations

Petr Tichý, Jan Zítko (1998)

Applications of Mathematics

Similarity:

Lanczos’ method for solving the system of linear algebraic equations A x = b consists in constructing a sequence of vectors x k in such a way that r k = b - A x k ∈ r 0 + A 𝒦 k ( A , r 0 ) and r k ⊥ 𝒦 k ( A T , r ˜ 0 ) . This sequence of vectors can be computed by the BiCG (BiOMin) algorithm. In this paper is shown how to obtain the recurrences of BiCG (BiOMin) directly from this conditions.