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The application of immersed boundary methods in static analyses is often impeded by poorly cut elements (small cut elements problem), leading to ill-conditioned linear systems of equations and stability problems. While these concerns may…

Singular value decomposition (SVD) is widely used for dimensionality reduction and noise suppression, and it plays a pivotal role in numerous scientific and engineering applications. As the dimensions of the matrix grow rapidly, the…

Stochastic differential equations (SDEs), which models uncertain phenomena as the time evolution of random variables, are exploited in various fields of natural and social sciences such as finance. Since SDEs rarely admit analytical…

In this paper, we present a novel semi-implicit numerical scheme for the stochastic Cahn--Hilliard equation driven by multiplicative noise. By reformulating the original equation into an equivalent stochastic scalar auxiliary variable…

Sparse triangular solve (SpTRSV) is widely used in various domains. Numerous studies have been conducted using CPUs, GPUs, and specific hardware accelerators, where dataflows can be categorized into coarse and fine granularity. Coarse…

In this paper, we concentrate on a particular category of quadratically constrained quadratic programming (QCQP): nonconvex QCQP with one equality constraint. This type of QCQP problem optimizes a quadratic objective under a fixed…

We study the algorithmic problem of estimating the mean of heavy-tailed random vector in $\mathbb{R}^d$, given $n$ i.i.d. samples. The goal is to design an efficient estimator that attains the optimal sub-gaussian error bound, only assuming…

The steady progress of quantum hardware is motivating the search for novel quantum algorithm optimization strategies for near-term, real-world applications. In this study, we propose a novel feature map optimization strategy for Quantum…

Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for…

3D registration has always been performed invoking singular value decomposition (SVD) or eigenvalue decomposition (EIG) in real engineering practices. However, these numerical algorithms suffer from uncertainty of convergence in many cases.…

The distributed adaptive signal fusion (DASF) framework allows to solve spatial filtering optimization problems in a distributed and adaptive fashion over a bandwidth-constrained wireless sensor network. The DASF algorithm requires each…

With growing deployment of Internet of Things (IoT) and machine learning (ML) applications, which need to leverage computation on edge and cloud resources, it is important to develop algorithms and tools to place these distributed…

In this paper, we report about recent findings in the numerical solution of Hamiltonian Partial Differential Equations (PDEs), by using energy-conserving line integral methods in the Hamiltonian Boundary Value Methods (HBVMs) class. In…

Energy efficiency (EE) is a challenging task in integrated sensing and communication (ISAC) systems, where high spectral efficiency and low energy consumption appear as conflicting requirements. Although passive reconfigurable intelligent…

In recent years, hardware-accelerated neural networks have gained significant attention for edge computing applications. Among various hardware options, crossbar arrays, offer a promising avenue for efficient storage and manipulation of…

Iterative methods on irregular grids have been used widely in all areas of comptational science and engineering for solving partial differential equations with complex geometry. They provide the flexibility to express complex shapes with…

Physical processes evolving in both time and space are often modeled using Partial Differential Equations (PDEs). Recently, it has been shown how stability analysis and control of coupled PDEs in a single spatial variable can be more…

Exact diagonalization (ED) is a cornerstone technique in quantum many-body physics, enabling precise solutions to the Schr\"odinger equation for interacting quantum systems. Despite its utility in studying ground states, excited states, and…

This article provides an effective computational algorithm based on Legendre wavelet (LW) and standard tau approach to approximate the solution of multi-dimensional distributed order time-space fractional weakly singular integro-partial…

We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…