Related papers: Acceleration of complex matrix multiplication usin…
This note presents fast Cholesky/LU/QR decomposition algorithms with $O(n^{2.529})$ time complexity when using the fastest known matrix multiplication. The algorithms have potential application, since a quickly made implementation using…
This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…
In 1969 Strassen showed surprisingly that it is possible to multiply two 2 x 2 matrices using seven multiplications and 18 additions, instead of the naive eight multiplications and four additions. The number of additions was later reduced…
Ootomo, Ozaki, and Yokota [Int. J. High Perform. Comput. Appl., 38 (2024), p. 297-313] have proposed a strategy to recast a floating-point matrix multiplication in terms of integer matrix products. The factors A and B are split into integer…
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…
Fast approximations to matrix multiplication have the potential to dramatically reduce the cost of neural network inference. Recent work on approximate matrix multiplication proposed to replace costly multiplications with table-lookups by…
This paper presents a new fast, highly scalable distributed matrix multiplication algorithm on Apache Spark, called Stark, based on Strassen's matrix multiplication algorithm. Stark preserves Strassen's 7 multiplications scheme in a…
In this paper, we report the results obtained from the acceleration of multi-binary64-type multiple precision matrix multiplication with AVX2. We target double-double (DD), triple-double (TD), and quad-double (QD) precision arithmetic…
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 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…
Clustering is one of the most fundamental and important tasks in data mining. Traditional clustering algorithms, such as K-means, assign every data point to exactly one cluster. However, in real-world datasets, the clusters may overlap with…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
The quest for non-commutative matrix multiplication algorithms in small dimensions has seen a lot of recent improvements recently. In particular, the number of scalar multiplications required to multiply two $4\times4$ matrices was first…
Accelerators for sparse matrix multiplication are important components in emerging systems. In this paper, we study the main challenges of accelerating Sparse Matrix Multiplication (SpMM). For the situations that data is not stored in the…
Graph analytics techniques based on spectral methods process extremely large sparse matrices with millions or even billions of non-zero values. Behind these algorithms lies the Top-K sparse eigenproblem, the computation of the largest…
We present two fast algorithms for matrix-vector multiplication $y=Ax$, where $A$ is a Hankel matrix. The current asymptotically fastest method is based on the Fast Fourier Transform (FFT), however in multiprecision arithmetics with very…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
An open-source C++ framework for discovering fast matrix multiplication schemes using the flip graph approach is presented. The framework supports multiple coefficient rings -- binary ($\mathbb{Z}_2$), modular ternary ($\mathbb{Z}_3$) and…
Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…
Cohn and Umans proposed a framework for developing fast matrix multiplication algorithms based on the embedding computation in certain groups algebras. In subsequent work with Kleinberg and Szegedy, they connected this to the search for…