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Quantum-dot cellular automata (QCA) shows promise as a post silicon CMOS, low power computational technology. Nevertheless, to generalize QCA for next-generation digital devices, the ability to implement conventional programmable circuits…

Mesoscale and Nanoscale Physics · Physics 2011-10-10 Joshua D. Wood , P. Douglas Tougaw

Floating point multiplication is a crucial operation in high power computing applications such as image processing, signal processing etc. And also multiplication is the most time and power consuming operation. This paper proposes an…

Hardware Architecture · Computer Science 2019-12-17 S Arish , R. K. Sharma

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…

Numerical Analysis · Mathematics 2024-04-24 Steffen Börm

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…

Machine Learning · Computer Science 2022-07-14 Calvin McCarter , Nicholas Dronen

Many fundamental problems in data mining can be reduced to one or more NP-hard combinatorial optimization problems. Recent advances in novel technologies such as quantum and quantum-inspired hardware promise a substantial speedup for…

Machine Learning · Computer Science 2022-01-10 Osman Asif Malik , Hayato Ushijima-Mwesigwa , Arnab Roy , Avradip Mandal , Indradeep Ghosh

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-08-29 Temitayo Adefemi

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,…

Numerical Analysis · Mathematics 2018-05-24 Jürgen Dölz , Helmut Harbrecht , Michael D. Multerer

This paper considers the problem of calculating the matrix multiplication of two massive matrices $\mathbf{A}$ and $\mathbf{B}$ distributedly. We provide a modulo technique that can be applied to coded distributed matrix multiplication…

Information Theory · Computer Science 2023-09-20 Zhiquan Tan , Dingli Yuan , Zihao Wang , Zhongyi Huang

This paper presents a low-latency hardware accelerator for modular polynomial multiplication for lattice-based post-quantum cryptography and homomorphic encryption applications. The proposed novel modular polynomial multiplier exploits the…

Cryptography and Security · Computer Science 2024-05-07 Weihang Tan , Antian Wang , Yingjie Lao , Xinmiao Zhang , Keshab K. Parhi

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…

Numerical Analysis · Mathematics 2026-05-11 Ahmad Abdelfattah , Jack Dongarra , Massimiliano Fasi , Mantas Mikaitis , Françoise Tisseur

Large-scale floating-point matrix multiplication is a fundamental kernel in many scientific and engineering applications. Most existing work only focus on accelerating matrix multiplication on FPGA by adopting a linear systolic array. This…

Hardware Architecture · Computer Science 2018-03-13 Junzhong Shen , Yuran Qiao , You Huang , Mei Wen , Chunyuan Zhang

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…

Symbolic Computation · Computer Science 2022-03-31 Pu Wu , Huiqing Jiang , Zehui Shao , Jin Xu

With the surge of the powerful quantum computer, lattice-based cryptography proliferated the latest cryptography hardware implementation due to its resistance against quantum computers. Among the computational blocks of lattice-based…

Cryptography and Security · Computer Science 2022-08-31 Antian Wang , Weihang Tan , Keshab K. Parhi , Yingjie Lao

We study the inversion analog of the well-known Gauss algorithm for multiplying complex matrices. A simple version is $(A + iB)^{-1} = (A + BA^{-1}B)^{-1} - i A^{-1}B(A+BA^{-1} B)^{-1}$ when $A$ is invertible, which may be traced back to…

Numerical Analysis · Mathematics 2023-10-10 Zhen Dai , Lek-Heng Lim , Ke Ye

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…

Numerical Analysis · Computer Science 2016-07-26 Grey Ballard , Austin R. Benson , Alex Druinsky , Benjamin Lipshitz , Oded Schwartz

In recent years, general matrix-matrix multiplication with non-regular-shaped input matrices has been widely used in many applications like deep learning and has drawn more and more attention. However, conventional implementations are not…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-01-24 Chendi Li , Haipeng Jia , Hang Cao , Jianyu Yao , Boqian Shi , Chunyang Xiang , Jinbo Sun , Pengqi Lu , Yunquan Zhang

An increasing number of applications are exploiting sampling-based algorithms for planning, optimization, and inference. The Markov Chain Monte Carlo (MCMC) algorithms form the computational backbone of this emerging branch of machine…

Machine Learning · Computer Science 2025-07-18 Shirui Zhao , Jun Yin , Lingyun Yao , Martin Andraud , Wannes Meert , Marian Verhelst

Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes ($\lesssim$ 5000), performance of traditional dense diagonalization algorithms on…

Chemical Physics · Physics 2023-06-23 Joshua Finkelstein , Christian F. A. Negre , Jean-Luc Fattebert

Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…

Information Theory · Computer Science 2019-05-17 Wei-Ting Chang , Ravi Tandon

This paper presents another improved version of Plantard arithmetic that could speed up Kyber implementations on two low-end 32-bit IoT platforms (ARM Cortex-M3 and RISC-V) without SIMD extensions. Specifically, we further enlarge the input…

Computers and Society · Computer Science 2024-02-20 Junhao Huang , Haosong Zhao , Jipeng Zhang , Wangchen Dai , Lu Zhou , Ray C. C. Cheung , Cetin Kaya Koc , Donglong Chen