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- Paolo Bientinesi, Inderjit S. Dhillon, Robert A. van de Geijn
- SIAM J. Scientific Computing
- 2005

- Paolo Bientinesi, Enrique S. Quintana-Ortí, Robert A. van de Geijn
- ACM Trans. Math. Softw.
- 2005

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)

- Paolo Bientinesi, John A. Gunnels, Margaret E. Myers, Enrique S. Quintana-Ortí, Robert A. van de Geijn
- ACM Trans. Math. Softw.
- 2005

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)

- Paolo Bientinesi
- 2006

- Matthias Petschow, Elmar Peise, Paolo Bientinesi
- SIAM J. Scientific Computing
- 2013

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)

- Jeffrey Napper, Paolo Bientinesi
- UCHPC-MAW '09
- 2009

Computing as a utility has reached the mainstream. Scientists can now rent time on large commercial clusters through several vendors. The cloud computing model provides flexible support for "pay as you go" systems. In addition to no upfront investment in large clusters or supercomputers, such systems incur no maintenance costs. Furthermore, they can be… (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)

- Paolo Bientinesi, Brian C. Gunter, Robert A. van de Geijn
- ACM Trans. Math. Softw.
- 2008

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)

- Field G. Van Zee, Paolo Bientinesi, Tze Meng Low, Robert A. van de Geijn
- ACM Trans. Math. Softw.
- 2008

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)

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)