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We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do…
Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including (W)CSP, DCOP, as well as optimization in stochastic…
Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…
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…
In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…
Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…
In this paper, an analytic approximation method for highly nonlinear equations, namely the homotopy analysis method (HAM), is employed to solve some backward stochastic differential equations (BSDEs) and forward-backward stochastic…
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering…
Dynamic simulators are computational models governed by differential equations that evolve over time. They are essential for scientific and engineering applications but remain challenging to emulate because of the unpredictable behavior of…
Physics-informed neural network (PINN) is a data-driven approach to solve equations. It is successful in many applications; however, the accuracy of the PINN is not satisfactory when it is used to solve multiscale equations. Homogenization…
This paper introduces generalized Bregman projection algorithms for solving nonlinear split feasibility problems (SF P s) in infinitedimensional Hilbert spaces. The methods integrate Bregman projections, proximal gradient steps, and…
Real-time trajectory optimization for nonlinear constrained autonomous systems is critical and typically performed by CPU-based sequential solvers. Specifically, reliance on global sparse linear algebra or the serial nature of dynamic…
A lot of real-world engineering problems represent dynamicity with nests of nonlinearities due to highly complex network of exponential functions or large number of differential equations interacting together. Such search spaces are…
Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. However, the estimation of the multiple nonlinear…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
The paper presents the aspect of use of modern graphics accelerators supporting CUDA technology for high-performance computing in the field of linear algebra. Fully programmable graphic cards have been available for several years for both…
Sparse Ising problems can be found in application areas such as logistics, condensed matter physics and training of deep Boltzmann networks, but can be very difficult to tackle with high efficiency and accuracy. This report presents new…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
This paper discusses the potential of graphics processing units (GPUs) in high-dimensional optimization problems. A single GPU card with hundreds of arithmetic cores can be inserted in a personal computer and dramatically accelerates many…
The rapid growth of large-scale machine learning (ML) models has led numerous commercial companies to utilize ML models for generating predictive results to help business decision-making. As two primary components in traditional predictive…