Related papers: Algebraic Temporal Blocking for Sparse Iterative S…
Dense, discrete Graphical Models with pairwise potentials are a powerful class of models which are employed in state-of-the-art computer vision and bio-imaging applications. This work introduces a new MAP-solver, based on the popular Dual…
HipMCL is a high-performance distributed memory implementation of the popular Markov Cluster Algorithm (MCL) and can cluster large-scale networks within hours using a few thousand CPU-equipped nodes. It relies on sparse matrix computations…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
This article presents a systematic quantitative performance analysis for large finite element computations on extreme scale computing systems. Three parallel iterative solvers for the Stokes system, discretized by low order tetrahedral…
This paper presents a novel symbolic algorithm for the Maximal End Component (MEC) decomposition of a Markov Decision Process (MDP). The key idea behind our algorithm INTERLEAVE is to interleave the computation of Strongly Connected…
The increasing number of processing elements and decreas- ing memory to core ratio in modern high-performance platforms makes efficient strong scaling a key requirement for numerical algorithms. In order to achieve efficient scalability on…
Large sparse symmetric linear systems appear in several branches of science and engineering thanks to the widespread use of the finite element method (FEM). The fastest sparse linear solvers available implement hybrid iterative methods.…
Matrix equations are omnipresent in (numerical) linear algebra and systems theory. Especially in model order reduction (MOR) they play a key role in many balancing based reduction methods for linear dynamical systems. When these systems…
In this article, cache blocking is implemented for the Navier Stokes equations with anti-aliasing support on mixed grids in PyFR for CPUs. In particular, cache blocking is used as an alternative to kernel fusion to eliminate unnecessary…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
An approach to obtaining a parsimonious polynomial model from time series is proposed. An optimal minimal nonuniform time series embedding schema is used to obtain a time delay kernel. This scheme recursively optimizes an objective…
Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…
Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are…
Sparse tiling is a technique to fuse loops that access common data, thus increasing data locality. Unlike traditional loop fusion or blocking, the loops may have different iteration spaces and access shared datasets through indirect memory…
Solving sparse linear systems is a critical challenge in many scientific and engineering fields, particularly when these systems are severely ill-conditioned. This work aims to provide a comprehensive comparison of various solvers designed…
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…
Sparse computations frequently appear in scientific simulations and the performance of these simulations rely heavily on the optimization of the sparse codes. The compact data structures and irregular computation patterns in sparse matrix…
Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to…
Sparse matrix-matrix multiplication (SpGEMM) is a critical operation in numerous fields, including scientific computing, graph analytics, and deep learning. These applications exploit the sparsity of matrices to reduce storage and…
We improve the current best running time value to invert sparse matrices over finite fields, lowering it to an expected $O\big(n^{2.2131}\big)$ time for the current values of fast rectangular matrix multiplication. We achieve the same…