Related papers: Dense Linear Algebra over Finite Fields: the FFLAS…
Countless applications cast their computational core in terms of dense linear algebra operations. These operations can usually be implemented by combining the routines offered by standard linear algebra libraries such as BLAS and LAPACK,…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
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…
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…
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)…
A major challenge in the deployment of scientific software solutions is the adaptation of research prototypes to production-grade code. While high-level languages like MATLAB are useful for rapid prototyping, they lack the resource…
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…
Most numerical solvers and libraries nowadays are implemented to use mathematical models created with language-specific built-in data types (e.g. real in Fortran or double in C) and their respective elementary algebra implementations.…
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…
Sparse linear algebra is central to many scientific programs, yet compilers fail to optimize it well. High-performance libraries are available, but adoption costs are significant. Moreover, libraries tie programs into vendor-specific…
In this work, we present the M4RIE library which implements efficient algorithms for linear algebra with dense matrices over GF(2^e) for 2 <= 2 <= 10. As the name of the library indicates, it makes heavy use of the M4RI library both…
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…
Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages) do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime…
We present here algorithms for efficient computation of linear algebra problems over finite fields.
The main purpose of this book is to propose an introduction to the modern tools of algebraic complexity. To remain as simple as possible while providing meaningful examples, we chose to focus on effective linear algebra; this is certainly…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
LAPACK and ScaLAPACK are arguably the defacto standard libraries among the scientific community for solving linear algebra problems on sequential, shared-memory and distributed-memory architectures. While ease of use was a major design goal…
Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…
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…
Basic Linear Algebra Subprograms (BLAS) is a core library in scientific computing and machine learning. This paper presents FT-BLAS, a new implementation of BLAS routines that not only tolerates soft errors on the fly, but also provides…