Expressions that involve matrices and vectors, known as linear algebra expressions, are commonly evaluated through a sequence of invocations to highly optimised kernels provided in libraries such as BLAS and LAPACK. A sequence of kernels represents an algorithm, and in general, because of associativity, algebraic identities, and multiple kernels, one expression can be evaluated via many different algorithms. These algorithms are all mathematically equivalent (i.e., in exact arithmetic, they all compute the same result), but often differ noticeably in terms of execution time. When faced with a decision, high-level languages, libraries, and tools such as Julia, Armadillo, and Linnea choose by selecting the algorithm that minimises the FLOP co...
This report has been developed over the work done in the deliverable [Nava94] There it was shown tha...
Cache-oblivious algorithms have been advanced as a way of circumventing some of the difficulties of ...
We consider the problem of developing formally correct dense linear algebra libraries. The problem ...
Expressions that involve matrices and vectors, known as linear algebra expressions, are commonly eva...
Expressions that involve matrices and vectors, known as linear algebra expressions, are commonly eva...
Linear algebra expressions, which play a central role in countless scientific computations, are ofte...
In this article we present a systematic approach to the derivation of families of high-performance a...
This dissertation introduces measurement-based performance modeling and prediction techniques for de...
This dissertation incorporates two research projects: performance modeling and prediction for dense ...
Abstract. In this article we look at the generation of libraries for dense linear algebra operations...
Abstract In this document we present a new approach to developing sequential and parallel dense line...
Abstract—It is well known that the behavior of dense linear algebra algorithms is greatly influenced...
Dense linear algebra computations are essential to nearly every problem in scientific computing and ...
textOver the last two decades, much progress has been made in the area of the high-performance sequ...
The goal of the LAPACK project is to provide efficient and portable software for dense numerical lin...
This report has been developed over the work done in the deliverable [Nava94] There it was shown tha...
Cache-oblivious algorithms have been advanced as a way of circumventing some of the difficulties of ...
We consider the problem of developing formally correct dense linear algebra libraries. The problem ...
Expressions that involve matrices and vectors, known as linear algebra expressions, are commonly eva...
Expressions that involve matrices and vectors, known as linear algebra expressions, are commonly eva...
Linear algebra expressions, which play a central role in countless scientific computations, are ofte...
In this article we present a systematic approach to the derivation of families of high-performance a...
This dissertation introduces measurement-based performance modeling and prediction techniques for de...
This dissertation incorporates two research projects: performance modeling and prediction for dense ...
Abstract. In this article we look at the generation of libraries for dense linear algebra operations...
Abstract In this document we present a new approach to developing sequential and parallel dense line...
Abstract—It is well known that the behavior of dense linear algebra algorithms is greatly influenced...
Dense linear algebra computations are essential to nearly every problem in scientific computing and ...
textOver the last two decades, much progress has been made in the area of the high-performance sequ...
The goal of the LAPACK project is to provide efficient and portable software for dense numerical lin...
This report has been developed over the work done in the deliverable [Nava94] There it was shown tha...
Cache-oblivious algorithms have been advanced as a way of circumventing some of the difficulties of ...
We consider the problem of developing formally correct dense linear algebra libraries. The problem ...