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In this article, we present a number of Application Program Interfaces (APIs) for coding linear algebra algorithms. On the surface, these APIs for the MATLAB M-script and C programming languages appear to be simple, almost trivial, extensions of those languages. Yet with them, the task of programming and maintaining families of algorithms for a broad… (More)

We introduce a new collection of solvers – subsequently called EleMRRR – for large-scale dense Hermitian eigenproblems. EleMRRR solves various types of problems: generalized, standard, and tridiagonal eigenproblems. Among these, the last is of particular importance as it is a solver on its own right, as well as the computational kernel for the first two; we… (More)

In this article we present a systematic approach to the derivation of families of high-performance algorithms for a large set of frequently encountered dense linear algebra operations. As part of the derivation a constructive proof of the correctness of the algorithm is generated. The article is structured so that it can be used as a tutorial for novices.… (More)

We discuss the OpenMP parallelization of linear algebra algorithms that are coded using the Formal Linear Algebra Methods Environment (FLAME) API. This API expresses algorithms at a higher level of abstraction, avoids the use loop and array indices, and represents these algorithms as they are formally derived and presented. We report on two implementations… (More)

This paper describes SuperMatrix, a runtime system that parallelizes matrix operations for SMP and/or multi-core architectures. We use this system to demonstrate how code described at a high level of abstraction can achieve high performance on such architectures while completely hiding the parallelism from the library programmer. The key insight entails… (More)

We present a new parallel algorithm for the dense symmetric eigenvalue/eigenvector problem that is based upon the tridiagonal eigensolver, Algorithm MR 3 , recently developed by Dhillon and Parlett. Algorithm MR 3 has a complexity of O(n 2) operations for computing all eigenvalues and eigenvectors of a symmetric tridiagonal problem. Moreover the algorithm… (More)

We study the high-performance implementation of the inversion of a Symmetric Positive Definite (SPD) matrix on architectures ranging from sequential processors to Symmetric MultiProcessors to distributed memory parallel computers. This inversion is traditionally accomplished in three “sweeps”: a Cholesky factorization of the SPD matrix, the… (More)

- Robert Van De Geijn, Todd Arbogast, Alan Cline, Calvin Lin, Paolo Bientinesi, M S Dissertation
- 2006

A Mamma e Babbo. In memory of Prof. Milvio Capovani, to whom I will always be indebted, for making me fall in love with matrix computations. Acknowledgments When discussing professors' advising styles, I point out that there is no one best style. It is the relationship between advisor and student that matters. In this respect, the relationship that I have… (More)

We investigate the performance of the routines in LAPACK and the Successive Band Reduction (SBR) toolbox for the reduction of a dense matrix to tridiagonal form, a crucial preprocessing stage in the solution of the symmetric eigenvalue problem. The target architecture is a current general purpose multi-core processor, where parallelism is extracted using a… (More)

In a series of papers it has been shown that for many linear algebra operations it is possible to generate families of algorithms by following a systematic procedure. Although powerful, such a methodology involves complex algebraic manipulation, symbolic computations and pattern matching, making the generation a process challenging to be performed by hand.… (More)