Related papers: Performance evaluation of accelerated complex mult…
In this work we present a variant of the fast multipole method (FMM) for efficiently evaluating standard layer potentials on geometries with complex coordinates in two and three dimensions. The complex scaled boundary integral method for…
It is well known that Strassen and Winograd algorithms can reduce the computational costs associated with dense matrix multiplication. We have already shown that they are also very effective for software-based multiple precision…
Accurately answering complex questions has consistently been a significant challenge for Large Language Models (LLMs). To address this, this paper proposes a multi-hop question decomposition method for complex questions, building upon…
In this work we describe an efficient implementation of a hierarchy of algorithms for the decomposition of dense matrices over the field with two elements (GF(2)). Matrix decomposition is an essential building block for solving dense…
Symmetric matrix decomposition is an active research area in machine learning. This paper focuses on exploiting the low-rank structure of non-negative and sparse symmetric matrices via the rectified linear unit (ReLU) activation function.…
The performance of numerical micromagnetic models is limited by the demagnetizing field computation, which typically accounts for the majority of the computation time. For magnetization dynamics simulations explicit evaluation methods are…
We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be…
In this paper, we study the following nonlinear matrix decomposition (NMD) problem: given a sparse nonnegative matrix $X$, find a low-rank matrix $\Theta$ such that $X \approx f(\Theta)$, where $f$ is an element-wise nonlinear function. We…
Debugging accumulation of floating-point errors is hard; ideally, computer should track it automatically. Here we consider twofold approximation of an exact real with value + error pair of floating-point numbers. Normally, value + error sum…
Efficient arithmetic circuit design for resourceconstrained hardware involves challenging combinatorial optimization problems, among which Multiple Constant Multiplication (MCM) is a prominent example. MCM aims at implementing…
Aiming at a drastic speedup for point-data embeddings at test time, we propose a new framework that uses a pair of multi-layer perceptron (MLP) and look-up table (LUT) to transform point-coordinate inputs into high-dimensional features.…
A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with $O(N \log^2 N)$…
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart of the algorithm is the evaluation of…
We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a…
In this paper we consider the application of direct methods for solving a sequence of saddle-point systems. Our goal is to design a method that reuses information from one factorization and applies it to the next one. In more detail, when…
Low-rank matrix approximation is extremely useful in the analysis of data that arises in scientific computing, engineering applications, and data science. However, as data sizes grow, traditional low-rank matrix approximation methods, such…
Matrix multiplication computation acceleration has been a research hotspot across various domains. Due to the characteristics of some applications, approximate matrix multiplication can achieve significant performance improvements without…
In spite of the great potential of large language models (LLMs) across various tasks, their deployment on resource-constrained devices remains challenging due to their excessive computational and memory demands. Quantization has emerged as…
Tucker decomposition is proposed to reduce the memory requirement of the far-fields in the fast multipole method (FMM)-accelerated surface integral equation simulators. It is particularly used to compress the far-fields of FMM groups, which…
The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…