Related papers: Parallel Cholesky Factorization for Banded Matrice…
Kernel methods represent some of the most popular machine learning tools for data analysis. Since exact kernel methods can be prohibitively expensive for large problems, reliable low-rank matrix approximations and high-performance…
We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block…
Systems of linear equations arise at the heart of many scientific and engineering applications. Many of these linear systems are sparse; i.e., most of the elements in the coefficient matrix are zero. Direct methods based on matrix…
The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…
Sparse linear algebra routines are fundamental building blocks of a large variety of scientific applications. Direct solvers, which are methods for solving linear systems via the factorization of matrices into products of triangular…
Kernel-based clustering algorithm can identify and capture the non-linear structure in datasets, and thereby it can achieve better performance than linear clustering. However, computing and storing the entire kernel matrix occupy so large…
This paper explores the performance optimization of out-of-core (OOC) Cholesky factorization on shared-memory systems equipped with multiple GPUs. We employ fine-grained computational tasks to expose concurrency while creating opportunities…
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…
We present three methods for distributed memory parallel inverse factorization of block-sparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and…
Algorithms come with multiple variants which are obtained by changing the mathematical approach from which the algorithm is derived. These variants offer a wide spectrum of performance when implemented on a multicore platform and we seek to…
Processors with large numbers of cores are becoming commonplace. In order to take advantage of the available resources in these systems, the programming paradigm has to move towards increased parallelism. However, increasing the level of…
In this note we briefly describe our Cholesky modification algorithm for streaming multiprocessor architectures. Our implementation is available in C++ with Matlab binding, using CUDA to utilise the graphics processing unit (GPU). Limited…
Direct factorization methods for the solution of large, sparse linear systems that arise from PDE discretizations are robust, but typically show poor time and memory scalability for large systems. In this paper, we describe an efficient…
This paper presents a GPU-accelerated framework for solving block tridiagonal linear systems that arise naturally in numerous real-time applications across engineering and scientific computing. Through a multi-stage permutation strategy…
We classify a family of matrices of shift operators that can be factorised in a computationally tractable manner with the Cholesky algorithm. Such matrices arise in the linear quadratic regulator problem, and related areas. We use the…
The algorithms in the current sequential numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multicore architectures. A new family of algorithms, the tile algorithms, has recently been introduced. Previous research…
We investigate a parallelization strategy for dense matrix factorization (DMF) algorithms, using OpenMP, that departs from the legacy (or conventional) solution, which simply extracts concurrency from a multithreaded version of BLAS. This…
In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered…
Matrix factorizations are among the most important building blocks of scientific computing. State-of-the-art libraries, however, are not communication-optimal, underutilizing current parallel architectures. We present novel algorithms for…
We present a new variant of serial right-looking supernodal sparse Cholesky factorization (RL). Our comparison of RL with the multifrontal method confirms that RL is simpler, slightly faster, and requires slightly less storage. The key to…