### Parallel Numerical Linear Algebra

#### Abstract

This special issue of Parallel and Distributed Computing Practices on *Parallel Numerical Linear Algebra* collects together a number of papers that address a range of important problems in the use of parallel computing in linear algebra. As parallel computing becomes the method of choice for solving our most changing problems it become more important to understand the interaction of various methods, architectures, and approaches to parallel computing.

The papers contained in this issue are summarized below:

Arbenz, Cleary, Dongarra and Hegland in *A comparison of parallel solvers for diagonally dominant and for general narrow banded linear systems* investigate stable parallel algorithms for solving banded systems of equations. The performance of the algorithms are compared with those of the ScaLAPACK parallel software. The results presented in the paper will be of interest to those who use parallel banded systems.

In *Mapping strategies in data parallel programming models; the projection methods* Emad considers the projection methods to solve large scale linear systems and eigenproblems. The paper first considers the data mapping of some projection methods. It then presents theoretical performance measures of data parallel algorithms and results obtained from experiments on the Connection Machine 5.

Parallel algorithms for multiplying a vector by a Kronecker tensor product of elementary matrices are discussed by Tadonki and Philippe in *Parallel multiplication of a vector by a Kronecker tensor product of matrices*. The derivation, complexity analyses and performances of the parallel algorithms are presented.

Zlatev and Georgiev in *Parallel sparse matrix algorithms for air pollution models* consider a parallel algorithm used in a large-scale air pollution model. The development, analysis and implementation of the algorithm is discussed in detail.

Besson in *Band preconditioners: application to preconditioned conjugate gradient methods on parallel computers* presents a divide and conquer method to solve band linear systems on parallel computers. The implementation and performance of the algorithm is discussed. The application of the method to the solution of Navier-Stokes equations in shallow domains is also presented.

Jack Dongarra, Tennessee, USA

Erricos John Kontoghiorghes, Neuchâ, Switzerland

#### References

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