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 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)
The challenge for the development of next generation software is the successful management of the complex computational environment while delivering to the scientist the full power of flexible compositions of the available algorithmic alternatives. Self-Adapting Numerical Software (SANS) systems are intended to meet this significant challenge. The process(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)
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 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.