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In this article, we propose an accuracy-assuring technique for finding a solution for unsymmetric linear systems. Such problems are related to different areas such as image processing, computer vision, and computational fluid dynamics.…
In this paper, we consider the dual formulation of minimizing $\sum_{i\in I}f_i(x_i)+\sum_{j\in J} g_j(\mathcal{A}_jx)$ with the index sets $I$ and $J$ being large. To address the difficulties from the high dimension of the variable $x$…
In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…
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…
The trend towards highly parallel multi-processing is ubiquitous in all modern computer architectures, ranging from handheld devices to large-scale HPC systems; yet many applications are struggling to fully utilise the multiple levels of…
Parallel transport is a fundamental tool to perform statistics on Rie-mannian manifolds. Since closed formulae don't exist in general, practitioners often have to resort to numerical schemes. Ladder methods are a popular class of algorithms…
Efficient multi-core parallel processing of recursive join queries is critical for achieving good performance in graph database management systems (GDBMSs). Prior work adopts two broad approaches. First is the state of the art morsel-driven…
The generalized eigenvalue problem (GEP) serves as a cornerstone in a wide range of applications in numerical linear algebra and scientific computing. However, traditional approaches that aim to maximize the classical Rayleigh quotient…
We propose a new scalable multi-class Gaussian process classification approach building on a novel modified softmax likelihood function. The new likelihood has two benefits: it leads to well-calibrated uncertainty estimates and allows for…
The Jacobi prior offers an alternative Bayesian framework, designed to achieve superior computational efficiency without compromising predictive performance. Compared to widely used methods such as Lasso, Ridge, Elastic Net, uniLasso, the…
This paper provides experimental experiences on two local search hybridized genetic algorithms in solving the uncapacitated examination timetabling problem. The proposed two hybrid algorithms use partition and priority based solution…
Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…
Based on an idea in Hironaka's proof of resolution of singularities, we present an algorithmic smoothness test for algebraic varieties. The test is inherently parallel and does not involve the calculation of codimension-sized minors of the…
Enumerating simple cycles has important applications in computational biology, network science, and financial crime analysis. In this work, we focus on parallelising the state-of-the-art simple cycle enumeration algorithms by Johnson and…
Image generation models have achieved widespread applications. As an instance, the TarFlow model combines the transformer architecture with Normalizing Flow models, achieving state-of-the-art results on multiple benchmarks. However, due to…
Multigrid methods have been a popular approach for solving linear systems arising from the discretization of partial differential equations (PDEs) for several decades. They are particularly effective for accelerating convergence rates with…
A hybrid-parallel direct-numerical-simulation method with application to turbulent Taylor-Couette flow is presented. The Navier-Stokes equations are discretized in cylindrical coordinates with the spectral Fourier-Galerkin method in the…
We describe a methodology for designing efficient parallel and distributed scientific software. This methodology utilizes sequences of mechanizable algebra--based optimizing transformations. In this study, we apply our methodology to the…
Iterative methods with certified convergence for the computation of Gauss--Jacobi quadratures are described. The methods do not require a priori estimations of the nodes to guarantee its fourth-order convergence. They are shown to be…
In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the…