251 Results Found

We proved the local Marchenko–Pastur law for sparse sample covariance matrices that corresponded to rectangular observation matrices of order $n\times m$ with $n/m\to y$ (where $y>0$) and sparse probability $n{p}_n>{log}^{\beta }n$ (where $\beta >0$)....

Despite the importance of sparse matrices in numerous fields of science, software implementations remain difficult to use for non-expert users, generally requiring the understanding of the underlying details of the chosen sparse matrix storage format...

Sparse matrix-vector multiplication (SpMV) can be used to solve diverse-scaled linear systems and eigenvalue problems that exist in numerous, and varying scientific applications. One of the scientific applications that SpMV is involved in is known as...

The sparse matrix–vector product (SpMV), considered one of the seven dwarfs (numerical methods of significance), is essential in high-performance real-world scientific and analytical applications requiring solution of large sparse linear equati...

Regression testing is a critical activity for maintaining software quality by identifying faults and ensuring system reliability. However, in large-scale software systems, executing all available test cases within limited time and computational resou...

In this paper, we introduce an efficient computational framework for pricing geometric Asian options based on a collocation method. The approach employs a collocation scheme utilizing a specific class of diagonal polynomials to construct operational...

We study estimation of globally sparse relation probability matrices from capped binary relation sets under personalized user-level local differential privacy and Byzantine response replacement. A cardinality-calibrated joint personalized relation sk...

Compressive Sensing (CS) is a transformative signal processing framework that enables sparse signal acquisition at rates below the Nyquist limit, offering substantial advantages in data efficiency and reconstruction accuracy. This survey explores the...

Winograd’s algorithms are an effective tool for calculating the discrete Fourier transform (DFT). These algorithms described in well-known articles are traditionally represented either with the help of sets of recurrent relations or with the he...

In the standardization of versatile video coding (VVC), discrete cosine transform (DCT)-2, discrete sine transform (DST)-7, and DCT-8 are regarded as the primary transform kernels. However, DST-4 and DCT-4 can also be considered as the transform kern...

Chaotic systems, with their characteristics of high sensitivity to initial conditions, pseudo-randomness, and ergodicity, provide high-quality pseudo-random sequences. Graph theory, through mechanisms such as vertex mapping, path traversal, and graph...

The upcoming technology of wide-swath altimetry from space will deliver a large volume of data on the ocean surface at unprecedentedly high spatial resolution. These data are contaminated by errors caused by the uncertainties in the geometry and orie...

Bayesian imaging algorithms are becoming increasingly important in, e.g., astronomy, medicine and biology. Given that many of these algorithms compute iterative solutions to high-dimensional inverse problems, the efficiency and accuracy of the instru...

Bayesian imaging algorithms are becoming increasingly important in, e.g., astronomy, medicine and biology. Given that many of these algorithms compute iterative solutions to high-dimensional inverse problems, the efficiency and accuracy of the instru...

At the heart of many computations in science and engineering lies the need to efficiently and accurately solve large sparse linear systems of equations. Direct methods are frequently the method of choice because of their robustness, accuracy and pote...

The aim of this survey is to review some recent developments in devising efficient preconditioners for sequences of symmetric positive definite (SPD) linear systems $A_k{\mathbf{x}}_k={\mathbf{b}}_k,k=1,\dots$ arising in many scientific applications, such...

An interesting question for linear programming (LP) algorithms is how to deal with solutions in which the number of nonzero variables is less than the number of rows of the matrix in standard form. An approach is that of basis deficiency-allowing (BD...

Process industries increasingly face large-scale nonlinear programs with high dimensionality and tight constraints. This study reports on the design and implementation of a reduced-space sequential quadratic programming (RSQP) solver for such setting...

This work aims to supplement the realization and validation of a higher-order well-balanced unstructured finite volume (FV) scheme, that has been relatively recently presented, for numerically simulating weakly non-linear weakly dispersive water wave...

The adoption of digital twins has revolutionized industrial process simulation, monitoring, and control effectiveness. However, practical implementations of digital twins are hindered by substantial challenges, including extended development time, di...

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We give an integer linear program formulation for the star bicolouring of bipartite graphs. We develop a column generation method to solve the linear programming relaxation to obtain a lower bound for the minimum number of colours needed. We determin...

To date, parallel simulation algorithms for spiking neural P (SNP) systems are based on a matrix representation. This way, the simulation is implemented with linear algebra operations, which can be easily parallelized on high performance computing pl...

In the paper, orthogonal transforms based on proposed symmetric, orthogonal matrices are created. These transforms can be considered as generalized Walsh–Hadamard Transforms. The simplicity of calculating the forward and inverse transforms is one of...

This paper investigates the spectral properties of block circulant matrices with high-order symmetric (or Hermitian) blocks. We analyze cases with dependent or sparse independent entries within these blocks. Additionally, we analyze the distribution...

A principal component analysis network (PCANet), as one of the representative deep subspace learning networks, utilizes principal component analysis (PCA) to learn filters that represent the dominant structural features of objects. However, the filte...

Sparse matrix–vector multiplication (SpMV) plays a significant role in the computational costs of many scientific applications such as 2D/3D robotics, power network problems, and computer vision. Numerous implementations using different sparse...

Sparse matrix–matrix multiplication (SpMM) is essential for deep learning models and scientific computing. Recently, Tensor Cores (TCs) on GPUs, originally designed for dense matrix multiplication with mixed precision, have gained prominence. H...

This study addresses the challenge of estimating high-dimensional covariance matrices in financial markets, where traditional sparsity assumptions often fail due to the interdependence of stock returns across sectors. We present an innovative element...

Low-rank sparse decomposition models have become the mainstream optimization framework for multiframe infrared small target detection. Existing low-rank matrix decomposition approximations typically pre-decompose infrared videos into the product of t...

This paper proposes an approach toward solving an issue pertaining to measuring compressible data in large-scale energy-harvesting wireless sensor networks with channel fading. We consider a scenario in which N sensors observe hidden phenomenon value...

In simulating Quantum Computing by using the circuit model the size of the matrices to deal with, together with the number of products and additions required to apply every quantum gate becomes a really hard computational restriction. This paper pres...

Grid renumbering techniques have been shown to be effective in improving the efficiency of computational fluid dynamics (CFD) numerical simulations based on the finite volume method (FVM). However, with the increasing complexity of real-world enginee...

Deep neural networks may achieve excellent performance in many research fields. However, many deep neural network models are over-parameterized. The computation of weight matrices often consumes a lot of time, which requires plenty of computing resou...

Optimizing sparse matrix–vector multiplication (SpMV) is challenging due to the non-uniform distribution of the non-zero elements of the sparse matrix. The best-performing SpMV format changes depending on the input matrix and the underlying arc...

Pruning and quantization are two commonly used approaches to accelerate the LSTM (Long Short-Term Memory) model. However, the traditional linear quantization usually suffers from the problem of gradient vanishing, and the existing pruning methods all...

Foeplitz and Loeplitz matrices are Toeplitz matrices with entries being Fibonacci and Lucas numbers, respectively. In this paper, explicit expressions of determinants and inverse matrices of Foeplitz and Loeplitz matrices are studied. Specifically, t...

Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix A and a recovery algorithm, such that the sparse...

Joint sparse representation has been widely used for hyperspectral image classification in recent years, however, the equal weight assigned to each neighbouring pixel is less realistic, especially for the edge areas, and one fixed scale is not approp...

The LU factorization of very large sparse matrices requires a significant amount of computing resources, including memory and broadband communication. A hybrid MPI + OpenMP + CUDA algorithm named SuperLU3D can efficiently compute the LU factorization...

Graphics processing units (GPUs) have delivered a remarkable performance for a variety of high performance computing (HPC) applications through massive parallelism. One such application is sparse matrix-vector (SpMV) computations, which is central to...

Spatial auto-regressive (SAR) models are widely used in geosciences for data analysis; their main feature is the presence of weight (W) matrices, which define the neighboring relationships between the spatial units. The statistical properties of para...

Chebyshev Wavelets of the third kind are proposed in this study to solve nonlinear systems of FDEs. The main goal of the method is to convert the nonlinear FDE into a nonlinear system of algebraic equations that can be easily solved using matrix meth...

In this paper, we extend the use of disjoint orthogonal components to three-way table analysis with the parallel factor analysis model. Traditional methods, such as scaling, orthogonality constraints, non-negativity constraints, and sparse techniques...

Due to resilience to background noise, stability of sparse reconstruction, and ability to capture local time-frequency information, the frame theory is becoming a dynamic forefront topic in data science. In this study, we overcome the disadvantages i...

Deep neural networks (DNNs) have been quite successful in solving many complex learning problems. However, DNNs tend to have a large number of learning parameters, leading to a large memory and computation requirement. In this paper, we propose a mod...

The recovery of the underlying low-rank structure of clean data corrupted with sparse noise/outliers is attracting increasing interest. However, in many low-level vision problems, the exact target rank of the underlying structure and the particular l...

Nowadays, as the number of items is increasing and the number of items that users have access to is limited, user-item preference matrices in recommendation systems are always sparse. This leads to a data sparsity problem. The latent factor analysis...

In this paper, a numerical approach for solving systems of nonlinear fractional differential equations (FDEs) is presented Using the Euler wavelets technique and associated operational matrices for fractional integration, we try to solve those system...

In this paper, fractional-order Bernoulli wavelets based on the Bernoulli polynomials are constructed and applied to evaluate the numerical solution of the general form of Caputo fractional order diffusion wave equations. The operational matrices of...