Related papers: A Short Note on Batch-efficient Divide-and-Conquer…
Edge computing's growing prominence, due to its ability to reduce communication latency and enable real-time processing, is promoting the rise of high-performance, heterogeneous System-on-Chip solutions. While current approaches often…
Due to importance of reducing of time solution in numerical codes, we propose an algorithm for parallel LU decomposition solver for dense and sparse matrices on GPU. This algorithm is based on first bi-vectorizing a triangular matrices of…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
Matrix decomposition is one of the fundamental tools to discover knowledge from big data generated by modern applications. However, it is still inefficient or infeasible to process very big data using such a method in a single machine.…
For dense Hermitian matrices with small off-diagonal (numerical) ranks and in a hierarchically semiseparable form, we give a stable divide-and-conquer eigendecomposition method with nearly linear complexity (called SuperDC) that…
In this paper, we show that the SVD of a matrix can be constructed efficiently in a hierarchical approach. Our algorithm is proven to recover the singular values and left singular vectors if the rank of the input matrix $A$ is known.…
Edge inference has become more widespread, as its diverse applications range from retail to wearable technology. Clusters of networked resource-constrained edge devices are becoming common, yet no system exists to split a DNN across these…
Quantum optimization as a field has largely been restricted by the constraints of current quantum computing hardware, as limitations on size, performance, and fidelity mean most non-trivial problem instances won't fit on quantum devices.…
Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3): A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix. For…
Gradient based optimization methods are the established state-of-the-art paradigm to study strongly entangled quantum systems in two dimensions with Projected Entangled Pair States. However, the key ingredient, the gradient itself, has…
We study faster algorithms for producing the minimum degree ordering used to speed up Gaussian elimination. This ordering is based on viewing the non-zero elements of a symmetric positive definite matrix as edges of an undirected graph, and…
Large collections of matrices arise throughout modern machine learning, signal processing, and scientific computing, where they are commonly compressed by concatenation followed by truncated singular value decomposition (SVD). This strategy…
The measure and conquer approach has proven to be a powerful tool to analyse exact algorithms for combinatorial problems, like Dominating Set and Independent Set. In this paper, we propose to use measure and conquer also as a tool in the…
Imaging Cherenkov detectors are largely used for particle identification (PID) in nuclear and particle physics experiments, where developing fast reconstruction algorithms is becoming of paramount importance to allow for near real time…
Multimodal retrieval still leans on embedding-based models like CLIP for fast vector search over pre-computed image embeddings. Yet, unlike text retrieval, where joint-encoder rerankers are standard, comparable vision-language rerankers are…
Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the…
Divide-and-conquer Bayesian methods consist of three steps: dividing the data into smaller computationally manageable subsets, running a sampling algorithm in parallel on all the subsets, and combining parameter draws from all the subsets.…
Sketching techniques have gained popularity in numerical linear algebra to accelerate the solution of least squares problems. The so-called $\varepsilon$-subspace embedding property of a sketching matrix $S$ has been largely used to…