Victor Eijkhout

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One of the main obstacles to the efficient solution of scientific problems is the problem of tuning software, both to the available architecture and to the user problem at hand. We describe approaches for obtaining tuned high-performance kernels, and for automatically choosing suitable algorithms. Specifically, we describe the generation of dense and sparse(More)
We have divided this book into five main chapters. Chapter 1 gives the motivation for this book and the use of templates. Chapter 2 describes stationary and nonstationary iterative methods. In this chapter we present both historical development and state-of-the-art methods for solving some of the most challenging computational problems facing researchers.(More)
Nested recursivetwo-level factorizationmethodsfor nine-pointdiierencematricesare analyzed. Somewhat similar in construction to multilevel methods for nite element matrices, these methods use recursive red-black orderings of the meshes, approximating the nine-point stencils by ve-point ones in the red points and then forming the reduced system explicitly.(More)
We survey the basic theory of the strengthened Cauchy-Buniakowskii-Schwarz inequality and its applications in multilevel methods for the solution of linear systems arising from nite element or nite diierence discretisation of elliptic partial diierential equations. Proofs are given both in a nite element context, and in purely algebraic form.
We present a method for automatically selecting optimal implementations of sparse matrixvector operations. Our software ‘AcCELS’ (Accelerated Compress-storage Elements for Linear Solvers) involves a setup phase that probes machine characteristics, and a run-time phase where stored characteristics are combined with a measure of the actual sparse matrix to(More)
Many fundamental and resource-intensive tasks in scientific computing, such as solving linear systems, can be approached through multiple algorithms. Using an algorithm well adapted to characteristics of the task can significantly enhance the performance by reducing resource utilization without compromising the quality of the result. Given the numerous(More)
This paper presents the conjugate gradient and Lanczos methods in a matrix framework, focusing mostly on orthogonality properties of the various vector sequences generated. Various aspects of the methods, such as choice of inner product, preconditioning, and relations to other iterative methods will be considered. Minimization properties of the methods and(More)
We propose a standard for storing metadata describing numerical matrix data. The standard consists of an XML file format and an internal data format. We give the abstract description of the XML storage format, APIs (Application Programmer Interfaces) for access to the stored data inside a program, and a core set of categories of data to be stored. The(More)