Related papers: On Parallelizing Matrix Multiplication by the Colu…
Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental computation in graph analytics, scientific simulation, and sparse deep learning workloads. However, the extreme irregularity of real-world sparse matrices prevents existing…
The multiplication of a sparse matrix with a dense vector (SpMV) is a key component in many numerical schemes and its performance is known to be severely limited by main memory access. Several numerical schemes require the multiplication of…
This paper proposes a frequent itemset mining algorithm based on the Boolean matrix method, aiming to solve the storage and computational bottlenecks of traditional frequent pattern mining algorithms in high-dimensional and large-scale…
In this paper, we propose a distributed framework for reducing the dimensionality of high-dimensional, large-scale, heterogeneous matrix-variate time series data using a factor model. The data are first partitioned column-wise (or row-wise)…
This paper presents a low-overhead optimizer for the ubiquitous sparse matrix-vector multiplication (SpMV) kernel. Architectural diversity among different processors together with structural diversity among different sparse matrices lead to…
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…
Algebraic multigrid (AMG) is an $\mathcal{O}(n)$ solution process for many large sparse linear systems. A hierarchy of progressively coarser grids is constructed that utilize complementary relaxation and interpolation operators. High-energy…
Straggler nodes are well-known bottlenecks of distributed matrix computations which induce reductions in computation/communication speeds. A common strategy for mitigating such stragglers is to incorporate Reed-Solomon based MDS (maximum…
Sparse matrix-vector multiplication (SpMxV) is a kernel operation widely used in iterative linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers. Matrices with irregular sparsity patterns make it…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
The use of large-scale machine learning methods is becoming ubiquitous in many applications ranging from business intelligence to self-driving cars. These methods require a complex computation pipeline consisting of various types of…
We propose a strategy for the generation of fast and accurate versions of non-commutative recursive matrix multiplication algorithms. To generate these algorithms, we consider matrix and tensor norm bounds governing the stability and…
Data for several applications in diverse fields can be represented as multiple matrices that are linked across rows or columns. This is particularly common in molecular biomedical research, in which multiple molecular "omics" technologies…
Sparse, irregular graphs show up in various applications like linear algebra, machine learning, engineering simulations, robotic control, etc. These graphs have a high degree of parallelism, but their execution on parallel threads of modern…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
Several applied problems may produce large sparse matrices with a small number of dense rows and/or columns, which can adversely affect the performance of commonly used direct solvers. By posing the problem as a saddle point system, an…
Most, if not all the modern scientific simulation packages utilize matrix algebra operations. Among the operation of the linear algebra, one of the most important kernels is the multiplication of matrices, dense and sparse. Examples of…
The matrix chain problem consists in finding the parenthesization of a matrix product $M := A_1 A_2 \cdots A_n$ that minimizes the number of scalar operations. In practical applications, however, one frequently encounters more complicated…
The method of choice to study one-dimensional strongly interacting many body quantum systems is based on matrix product states and operators. Such method allows to explore the most relevant, and numerically manageable, portion of an…
We consider irregular product codes.In this class of codes, each codeword is represented by a matrix. The entries in each row (column) of the matrix should come from a component row (column) code. As opposed to (standard) product codes, we…