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In this paper, we present an efficient semismooth Newton method, named SSNCP, for solving a class of semidefinite programming problems. Our approach is rooted in an equivalent semismooth system derived from the saddle point problem induced…
We present a methodology for parallel acceleration of learning in the presence of matrix orthogonality and unitarity constraints of interest in several branches of machine learning. We show how an apparently sequential elementary rotation…
A q-Gauss-Newton algorithm is an iterative procedure that solves nonlinear unconstrained optimization problems based on minimization of the sum squared errors of the objective function residuals. Main advantage of the algorithm is that it…
Interior Point Methods (IPM) rely on the Newton method for solving systems of nonlinear equations. Solving the linear systems which arise from this approach is the most computationally expensive task of an interior point iteration. If, due…
Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs,…
Algorithm learning is a core problem in artificial intelligence with significant implications on automation level that can be achieved by machines. Recently deep learning methods are emerging for synthesizing an algorithm from its…
This paper proposes a combination of a hybrid CPU--GPU and a pure GPU software implementation of a direct algorithm for solving shifted linear systems $(A - \sigma I)X = B$ with large number of complex shifts $\sigma$ and multiple…
This paper focuses on the parallel implementation of a direct $N$-body method~(particle-particle algorithm) and the application of multiple GPUs for galactic dynamics simulations. Application of a hybrid OpenMP-CUDA technology is considered…
Quantum machine learning techniques have been proposed as a way to potentially enhance performance in machine learning applications. In this paper, we introduce two new quantum methods for neural networks. The first one is a quantum…
In this paper we solve on GPUs massive problems with large amount of data, which are not appropriate for solution with the SIMD technology. For the given problem we consider a three-level parallelization. The multithreading of CPU is used…
Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…
GPUs have significantly accelerated first-order methods for large-scale optimization, especially in continuous optimization. However, this success has not transferred cleanly to problems with discrete variables, combinatorial structure, and…
In this paper we present a methodology for data accesses when solving batches of Tridiagonal and Pentadiagonal matrices that all share the same left-hand-side (LHS) matrix. The intended application is to the numerical solution of Partial…
In partial differential equations-based (PDE-based) inverse problems with many measurements, many large-scale discretized PDEs must be solved for each evaluation of the misfit or objective function. In the nonlinear case, evaluating the…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
We are concerned with the fastest possible direct numerical solution algorithm for a thin-banded or tridiagonal linear system of dimension $N$ on a distributed computing network of $N$ nodes that is connected in a binary communication tree.…
Edge intelligence has arisen as a promising computing paradigm for supporting miscellaneous smart applications that rely on machine learning techniques. While the community has extensively investigated multi-tier edge deployment for…
The IEEE 754-2008 standard recommends the correct rounding of some elementary functions. This requires to solve the Table Maker's Dilemma which implies a huge amount of CPU computation time. We consider in this paper accelerating such…
Basing on a modification of the "Dichotomy Algorithm" (Terekhov, 2010), we propose a parallel procedure for solving tridiagonal systems of equations with Toeplitz matrices. Taking the structure of the Toeplitz matrices, we may substantially…
A high-order Newton multigrid method is proposed for steady-state shallow water flows in open channels with regular and irregular geometries. The method integrates a finite volume discretization with third-order weighted essentially…