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We propose a fast collocation method based on Krylov subspace iterative solver on general nonuniform grids for the fractional Laplacian problem, in which the fractional operator is presented in a singular integral formulation. The method is…

Numerical Analysis · Mathematics 2025-11-13 Meijie Kong , Hongfei Fu

Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…

As an important technology in artificial intelligence Granular Computing (GrC) has emerged as a new multi-disciplinary paradigm and received much attention in recent years. Information granules forming an abstract and efficient…

Machine Learning · Computer Science 2020-04-10 Kaijie Xu , Witold Pedrycz , Zhiwu Li , Mengdao Xing

Deflation techniques for Krylov subspace methods have seen a lot of attention in recent years. They provide means to improve the convergence speed of these methods by enriching the Krylov subspace with a deflation subspace. The most common…

Numerical Analysis · Mathematics 2017-04-26 K. Kahl , H. Rittich

We develop a novel randomized conjugate gradient least squares (RCGLS) method for solving least-squares problems, in which iterative sketching is employed at each step to reduce the dimension and hence the computational cost. In particular,…

Numerical Analysis · Mathematics 2026-05-26 Yun Zeng , Jian-Feng Cai , Deren Han , Jiaxin Xie

We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…

Optimization and Control · Mathematics 2019-02-19 Daniela di Serafino , Gerardo Toraldo , Marco Viola , Jesse Barlow

The Gromov-Wasserstein distance is a notable extension of optimal transport. In contrast to the classic Wasserstein distance, it solves a quadratic assignment problem that minimizes the pair-wise distance distortion under the transportation…

Machine Learning · Computer Science 2024-04-16 Wei Zhang , Zihao Wang , Jie Fan , Hao Wu , Yong Zhang

Scalable spatial GPs for massive datasets can be built via sparse Directed Acyclic Graphs (DAGs) where a small number of directed edges is sufficient to flexibly characterize spatial dependence. The DAG can be used to devise fast algorithms…

Methodology · Statistics 2025-03-31 Michele Peruzzi , Sudipto Banerjee , David B. Dunson , Andrew O. Finley

A recent article introduced thecontinuous stochastic gradient method (CSG) for the efficient solution of a class of stochastic optimization problems. While the applicability of known stochastic gradient type methods is typically limited to…

Optimization and Control · Mathematics 2021-11-16 Lukas Pflug , Max Grieshammer , Andrian Uihlein , Michael Stingl

A cascadic multigrid method is proposed for the GPE problem based on the multilevel correction scheme. With this new scheme, the ground state eigenvalue problem on the finest space can be solved by smoothing steps on a series of multilevel…

Numerical Analysis · Mathematics 2015-04-22 Xiaole Han , Hehu Xie

Coarse-grained (CG) molecular dynamics (MD) simulations can simulate large molecular complexes over extended timescales by reducing degrees of freedom. A critical step in CG modeling is the selection of the CG mapping algorithm, which…

Soft Condensed Matter · Physics 2025-07-23 Soumya Mondal , Subhanu Halder , Debarchan Basu , Sandeep Kumar , Tarak Karmakar

The combinatorial integral approximation (CIA) is a solution technique for integer optimal control problems. In order to regularize the solutions produced by CIA, one can minimize switching costs in one of its algorithmic steps. This leads…

Optimization and Control · Mathematics 2023-05-23 Felix Bestehorn , Christoph Hansknecht , Christian Kirches , Paul Manns

Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…

Numerical Analysis · Mathematics 2021-05-18 Jennifer A. Loe , Christian A. Glusa , Ichitaro Yamazaki , Erik G. Boman , Sivasankaran Rajamanickam

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

Machine Learning · Statistics 2025-11-26 Jonas Latz , Aretha L. Teckentrup , Simon Urbainczyk

A grouping-circular-based (GCB) greedy algorithm is proposed to promote the efficiency of mesh deformation. By incorporating the multigrid concept that the computational errors on the fine mesh can be approximated with those on the coarse…

Numerical Analysis · Mathematics 2021-03-17 Hong Fang , He Zhang , Fanli Shan , Ming Tie , Xing Zhang , Jinghua Sun

Solving partial differential equations is crucial to analysing and predicting complex, large-scale physical systems but pushes conventional high-performance computers to their limits. Application specific photonic processors are an exciting…

Computational Physics · Physics 2025-11-04 Timoteo Lee , Frank Brückerhoff-Plückelmann , Jelle Dijkstra , Jan M. Pawlowski , Wolfram Pernice

We present an efficient, robust and fully GPU-accelerated aggregation-based algebraic multigrid preconditioning technique for the solution of large sparse linear systems. These linear systems arise from the discretization of elliptic PDEs.…

Numerical Analysis · Mathematics 2014-03-10 Rajesh Gandham , Ken Esler , Yongpeng Zhang

Generalized cross validation (GCV) is one of the most important approaches used to estimate parameters in the context of inverse problems and regularization techniques. A notable example is the determination of the smoothness parameter in…

Machine Learning · Statistics 2017-06-09 Giulio Bottegal , Gianluigi Pillonetto

Iteratively Re-weighted Least Squares (IRLS) is a method for solving minimization problems involving non-quadratic cost functions, perhaps non-convex and non-smooth, which however can be described as the infimum over a family of quadratic…

Numerical Analysis · Mathematics 2016-02-24 Massimo Fornasier , Steffen Peter , Holger Rauhut , Stephan Worm

This work deals with tailored reduced order models for bifurcating nonlinear parametric partial differential equations, where multiple coexisting solutions arise for a given parametric instance. Approaches based on proper orthogonal…

Numerical Analysis · Mathematics 2025-05-14 Federico Pichi , Maria Strazzullo