Book,
Templates for the Solution of Linear Systems : Building Blocks for Iterative Methods
Other Titles in Applied Mathematics Society for Industrial and Applied Mathematics, 1 edition, (Jan 1, 1987)
DOI: 10.1137/1.9781611971538
Abstract
In this book, which focuses on the use of iterative methods for solving large
sparse systems of linear equations, templates are introduced to meet the needs
of both the traditional user and the high-performance specialist. Templates, a
description of a general algorithm rather than the executable object or source
code more commonly found in a conventional software library, offer whatever degree of customization the user may desire.
Templates have three distinct advantages: they are general and reusable, they
are not language specific, and they exploit the expertise of both the numerical analyst, who creates a template reflecting in-depth knowledge of a specific numerical technique, and the computational scientist, who then
provides "value-added" capability to the general template description, customizing it for specific needs. For each template that is presented, the authors provide a mathematical description of the flow of the algorithm, discussion of convergence and stopping criteria to use in the iteration,
suggestions for applying a method to special matrix types, advice for tuning the template, tips on parallel implementations, and hints as to when and why a method is useful.
