Related papers: A Parallel Algorithm for Calculation of Large Dete…
This paper proposes a scalable binary CUR low-rank approximation algorithm that leverages parallel selection of representative rows and columns within a deterministic framework. By employing a blockwise adaptive cross approximation…
This paper presents a well-scaling parallel algorithm for the computation of Morse-Smale (MS) segmentations, including the region separators and region boundaries. The segmentation of the domain into ascending and descending manifolds,…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
A hybrid MPI+OpenMP strategy for parallelizing multiple precision Taylor series method is proposed, realized and tested. To parallelize the algorithm we combine MPI and OpenMP parallel technologies together with GMP library (GNU miltiple…
We propose a new practical algorithm for computing the Feigenbaum constants {\alpha} and {\delta}, having significantly lower time and space complexity than previously used methods. The algorithm builds upon well-known linear algebra…
We present an optimized version of a cluster labeling algorithm previously introduced by the authors. This algorithm is well suited for large-scale Monte Carlo simulations of spin models using cluster dynamics on parallel computers with…
Recently, Deep Neural Networks (DNNs) have recorded great success in handling medical and other complex classification tasks. However, as the sizes of a DNN model and the available dataset increase, the training process becomes more complex…
The latent block model is used to simultaneously rank the rows and columns of a matrix to reveal a block structure. The algorithms used for estimation are often time consuming. However, recent work shows that the log-likelihood ratios are…
Nonlinearities in the gravitational evolution, galaxy bias, and redshift-space distortion drive the observed galaxy density fields away from the initial near-Gaussian states. Exploiting such a non-Gaussian galaxy density field requires…
The optimization of submodular functions constitutes a viable way to perform clustering. Strong approximation guarantees and feasible optimization w.r.t. streaming data make this clustering approach favorable. Technically, submodular…
Several classic problems in graph processing and computational geometry are solved via incremental algorithms, which split computation into a series of small tasks acting on shared state, which gets updated progressively. While the…
Training large language models (LLMs) is known to be challenging because of the huge computational and memory capacity requirements. To address these issues, it is common to use a cluster of GPUs with 3D parallelism, which splits a model…
The problem of automatically clustering data is an age old problem. People have created numerous algorithms to tackle this problem. The execution time of any of this algorithm grows with the number of input points and the number of cluster…
We present a computational algorithm for computing short range forces between particles. The algorithm has two distinguishing features. First, it is optimized for multi-processor computers, and will use as many processors as are available.…
This problem was solved within the framework of the grant project "Solving of problems of cluster analysis with application of parallel algorithms and cloud technologies" in the Institute of Mathematics and Mathematical Modelling in Almaty.…
Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…
The discrete distribution clustering algorithm, namely D2-clustering, has demonstrated its usefulness in image classification and annotation where each object is represented by a bag of weighed vectors. The high computational complexity of…
We present and evaluate GPU Bucket Sort, a parallel deterministic sample sort algorithm for many-core GPUs. Our method is considerably faster than Thrust Merge (Satish et.al., Proc. IPDPS 2009), the best comparison-based sorting algorithm…
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple…
We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…