Related papers: Hierarchical Performance Modeling for Ranking Dens…
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…
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,…
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…
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…
We provide a multilevel approach for analysing performances of parallel algorithms. The main outcome of such approach is that the algorithm is described by using a set of operators which are related to each other according to the problem…
We study algorithms for estimating the statistical leverage scores of rectangular dense or sparse matrices of arbitrary rank. Our approach is based on combining rank revealing methods with compositions of dense and sparse randomized…
A common way of doing algorithm selection is to train a machine learning model and predict the best algorithm from a portfolio to solve a particular problem. While this method has been highly successful, choosing only a single algorithm has…
Linear algebra expressions, which play a central role in countless scientific computations, are often computed via a sequence of calls to existing libraries of building blocks (such as those provided by BLAS and LAPACK). A sequence…
We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…
We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be…
Multilinear algebra kernel performance on modern massively-parallel systems is determined mainly by data movement. However, deriving data movement-optimal distributed schedules for programs with many high-dimensional inputs is a notoriously…
In this work an efficient algorithm to perform a block decomposition (and so to compute the rank) of large dense rectangular matrices with entries in $\mathbb{F}_2$ is presented. Depending on the way the matrix is stored, the operations…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
We present novel algorithmic techniques to efficiently verify the Kruskal rank of matrices that arise in sparse linear regression, tensor decomposition, and latent variable models. Our unified framework combines randomized hashing…
In scientific computing, it is common that a mathematical expression can be computed by many different algorithms (sometimes over hundreds), each identifying a specific sequence of library calls. Although mathematically equivalent, those…
Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. However, a public benchmark with appropriate performance metrics for…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To…
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…