Related papers: A Short Note on Batch-efficient Divide-and-Conquer…

EigenDecomposition (ED) is at the heart of many computer vision algorithms and applications. One crucial bottleneck limiting its usage is the expensive computation cost, particularly for a mini-batch of matrices in the deep neural networks.…

Eigendecomposition (ED) is widely used in deep networks. However, the backpropagation of its results tends to be numerically unstable, whether using ED directly or approximating it with the Power Iteration method, particularly when dealing…

Divide-and-conquer-based (DC-based) evolutionary algorithms (EAs) have achieved notable success in dealing with large-scale optimization problems (LSOPs). However, the appealing performance of this type of algorithms generally requires a…

Divide and Conquer (D&C) is a widely used algorithmic strategy for symmetric eigenvalue decomposition. Its natural parallelism makes D&C attractive on modern multicore CPUs and GPUs, but existing eigenvalue-only routines often default to…

Eigensystem Realization Algorithm (ERA) is a data-driven approach for subspace system identification and is widely used in many areas of engineering. However, the computational cost of the ERA is dominated by a step that involves the…

The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…

Spectral clustering is one of the most popular clustering methods. However, how to balance the efficiency and effectiveness of the large-scale spectral clustering with limited computing resources has not been properly solved for a long…

Deep learning models are increasingly utilized on resource-constrained edge devices for real-time data analytics. Recently, Vision Transformer and their variants have shown exceptional performance in various computer vision tasks. However,…

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for…

In this paper, two accelerated divide-and-conquer algorithms are proposed for the symmetric tridiagonal eigenvalue problem, which cost $O(N^2r)$ {flops} in the worst case, where $N$ is the dimension of the matrix and $r$ is a modest number…

Singular Value Decomposition (SVD) is a fundamental matrix factorization technique in linear algebra, widely applied in numerous matrix-related problems. However, traditional SVD approaches are hindered by slow panel factorization and…

In this paper, we describe a low-rank matrix completion method based on matrix decomposition. An incomplete matrix is decomposed into submatrices which are filled with a proposed trimming step and then are recombined to form a low-rank…

Convolution is a critical component in modern deep neural networks, thus several algorithms for convolution have been developed. Direct convolution is simple but suffers from poor performance. As an alternative, multiple indirect methods…

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector…

Computing eigenvalue decomposition (EVD) of a given linear operator, or finding its leading eigenvalues and eigenfunctions, is a fundamental task in many machine learning and scientific computing problems. For high-dimensional eigenvalue…

Recurrent neural networks can be large and compute-intensive, yet many applications that benefit from RNNs run on small devices with very limited compute and storage capabilities while still having run-time constraints. As a result, there…

We propose a distributed computing framework, based on a divide and conquer strategy and hierarchical modeling, to accelerate posterior inference for high-dimensional Bayesian factor models. Our approach distributes the task of…

Supervised cross-modal hashing has gained increasing research interest on large-scale retrieval task owning to its satisfactory performance and efficiency. However, it still has some challenging issues to be further studied: 1) most of them…

Benefiting from the advancement of hardware accelerators such as GPUs, deep neural networks and scientific computing applications can achieve superior performance. Recently, the computing capacity of emerging hardware accelerators has…

Motivation: Surface generation and visualization are some of the most important tasks in biomolecular modeling and computation. Eulerian solvent excluded surface (ESES) software provides analytical solvent excluded surface (SES) in the…