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It is well known that the behavior of dense linear algebra algorithms is greatly influenced by factors like target architecture, underlying libraries and even problem size; because of this, the accurate prediction of their performance is a…
This dissertation introduces measurement-based performance modeling and prediction techniques for dense linear algebra algorithms. As a core principle, these techniques avoid executions of such algorithms entirely, and instead predict their…
A large class of dense linear algebra operations, such as LU decomposition or inversion of a triangular matrix, are usually performed by blocked algorithms. For one such operation, typically, not only one but many algorithmic variants…
Optimal use of computing resources requires extensive coding, tuning and benchmarking. To boost developer productivity in these time consuming tasks, we introduce the Experimental Linear Algebra Performance Studies framework (ELAPS), a…
To exploit both memory locality and the full performance potential of highly tuned kernels, dense linear algebra libraries such as LAPACK commonly implement operations as blocked algorithms. However, to achieve next-to-optimal performance…
It is universally known that caching is critical to attain high- performance implementations: In many situations, data locality (in space and time) plays a bigger role than optimizing the (number of) arithmetic floating point operations. In…
Dijkstra observed that verifying correctness of a program is difficult and conjectured that derivation of a program hand-in-hand with its proof of correctness was the answer. We illustrate this goal-oriented approach by applying it to the…
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…
This paper advocates for an intertwined design of the dense linear algebra software stack that breaks down the strict barriers between the high-level, blocked algorithms in LAPACK (Linear Algebra PACKage) and the low-level,…
Dealing with asymmetry in the architecture opens a plethora of questions from the perspective of scheduling task-parallel applications, and there exist early attempts to address this problem via ad-hoc strategies embedded into a runtime…
Linear algebra operations, which are ubiquitous in machine learning, form major performance bottlenecks. The High-Performance Computing community invests significant effort in the development of architecture-specific optimized kernels, such…
This work introduces CLBlast, an open-source BLAS library providing optimized OpenCL routines to accelerate dense linear algebra for a wide variety of devices. It is targeted at machine learning and HPC applications and thus provides a fast…
Query performance prediction, the task of predicting the latency of a query, is one of the most challenging problem in database management systems. Existing approaches rely on features and performance models engineered by human experts, but…
Hiding or minimizing the communication cost is key in order to obtain good performance on large-scale systems. While communication overlapping attempts to hide communications cost, 2.5D communication avoiding algorithms improve performance…
Linear algebra algorithms are used widely in a variety of domains, e.g machine learning, numerical physics and video games graphics. For all these applications, loop-level parallelism is required to achieve high performance. However,…
Tensor operations are surging as the computational building blocks for a variety of scientific simulations and the development of high-performance kernels for such operations is known to be a challenging task. While for operations on one-…
Dense linear algebra libraries, such as BLAS and LAPACK, provide a relevant collection of numerical tools for many scientific and engineering applications. While there exist high performance implementations of the BLAS (and LAPACK)…
In this paper, we tackle the problem of automatically generating algorithms for linear algebra operations by taking advantage of problem-specific knowledge. In most situations, users possess much more information about the problem at hand…
The translation of linear algebra computations into efficient sequences of library calls is a non-trivial task that requires expertise in both linear algebra and high-performance computing. Almost all high-level languages and libraries for…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…