Related papers: Hyper-Systolic Matrix Multiplication
We generalize the hyper-systolic algorithm proposed in [1] for abstract data structures on massive parallel computers with $n_p$ processors. For a problem of size $V$ the communication complexity of the hyper-systolic algorithm is…
Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an…
A new class of parallel algorithms is introduced that can achieve a complexity of O(n^3/2) with respect to the interprocessor communication, in the exact computation of systems with pairwise mutual interactions of all elements. Hitherto,…
In recent years, with the rapid development of electro-optic modulators, optical computing has become a potential excellent candidate for various computing tasks. New structures and devices for optical computing are emerging one after…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
A novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths…
Matrix multiplication is integral to various scientific and engineering disciplines, including machine learning, image processing, and gaming. With the increasing data volumes in areas like machine learning, the demand for efficient…
Computation of a signal's estimated covariance matrix is an important building block in signal processing, e.g., for spectral estimation. Each matrix element is a sum of products of elements in the input matrix taken over a sliding window.…
Sparse matrix multiplication is an important component of linear algebra computations. Implementing sparse matrix multiplication on an associative processor (AP) enables high level of parallelism, where a row of one matrix is multiplied in…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
In this paper, we consider the HLS implementation of a three-dimensional systolic array architecture for matrix multiplication that targets specific characteristics of Intel Stratix 10 FPGAs in order to produce designs that achieve a high…
Multiplication of a sparse matrix with another (dense or sparse) matrix is a fundamental operation that captures the computational patterns of many data science applications, including but not limited to graph algorithms, sparsely connected…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
We design and develop a work-efficient multithreaded algorithm for sparse matrix-sparse vector multiplication (SpMSpV) where the matrix, the input vector, and the output vector are all sparse. SpMSpV is an important primitive in the…
We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of…
An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The…
In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…