A practical preconditioner for sparse banded linear systems

Abstract

In this short note the determination of a practical preconditioner for sparse banded matrices is outlined. Such matrices occur in the discretisation of partial differential equations by finite difference/element techniques or in approximation problems involving collocution or wavelet strategies.

However since such matrices are often illconditioned and of large order the need of an easily derived and practical preconditioner to provide rapid convergence for the chosen iterative method is paramount. The analysis is supported by numerical experiments.

Keywords:

• Sparse banded matrix
• Precondition parameter