Related papers: Fast and Practical Strassen's Matrix Multiplicatio…
Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due…
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…
The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate single- as well as…
While Strassen's matrix multiplication algorithm reduces the complexity of naive matrix multiplication, general-purpose hardware is not suitable for achieving the algorithm's promised theoretical speedups. This leaves the question of if it…
Recently, reinforcement algorithms discovered new algorithms that really jump-started a wave of excitements and a flourishing of publications. However, there is little on implementations, applications, and, especially, no absolute…
Matrix multiplication is a fundamental kernel in high performance computing. Many algorithms for fast matrix multiplication can only be applied to enormous matrices ($n>10^{100}$) and thus cannot be used in practice. Of all algorithms…
It is known that the multiplication of an $N \times M$ matrix with an $M \times P$ matrix can be performed using fewer multiplications than what the naive $NMP$ approach suggests. The most famous instance of this is Strassen's algorithm for…
Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few…
Matrix multiplication $A^t A$ appears as intermediate operation during the solution of a wide set of problems. In this paper, we propose a new cache-oblivious algorithm for the $A^t A$ multiplication. Our algorithm, A$\scriptstyle…
We dispel with "street wisdom" regarding the practical implementation of Strassen's algorithm for matrix-matrix multiplication (DGEMM). Conventional wisdom: it is only practical for very large matrices. Our implementation is practical for…
Obeying constraints imposed by classical physics, we give optimal fine-grained algorithms for matrix multiplication and problems involving graphs and mazes, where all calculations are done in 3-dimensional space. We assume that whatever the…
Fast matrix multiplication can be described as searching for low-rank decompositions of the matrix--multiplication tensor. We design a neural architecture, \textsc{StrassenNet}, which reproduces the Strassen algorithm for $2\times 2$…
A tight $\Omega((n/\sqrt{M})^{\log_2 7}M)$ lower bound is derived on the \io complexity of Strassen's algorithm to multiply two $n \times n$ matrices, in a two-level storage hierarchy with $M$ words of fast memory. A proof technique is…
Large matrix multiplication is a cornerstone of modern machine learning workloads, yet traditional approaches suffer from cubic computational complexity (e.g., $\mathcal{O}(n^3)$ for a matrix of size $n\times n$). We present Low-Rank GEMM,…
Conventional GPU implementations of Strassen's algorithm (Strassen) typically rely on the existing high-performance matrix multiplication (GEMM), trading space for time. As a result, such approaches can only achieve practical speedup for…
Efficient multiple precision linear numerical computation libraries such as MPLAPACK are critical in dealing with ill-conditioned problems. Specifically, there are optimization methods for matrix multiplication, such as the Strassen…
After Strassen presented the first sub-cubic matrix multiplication algorithm, many Strassen-like algorithms are presented. Most of them with low asymptotic cost have large hidden leading coefficient which are thus impractical. To reduce the…
In this study, we propose a simple method for fault-tolerant Strassen-like matrix multiplications. The proposed method is based on using two distinct Strassen-like algorithms instead of replicating a given one. We have realized that using…
Parallel matrix multiplication is one of the most studied fundamental problems in distributed and high performance computing. We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes…
General Matrix Multiplication (GEMM) is a fundamental operation widely used in scientific computations. Its performance and accuracy significantly impact the performance and accuracy of applications that depend on it. One such application…