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Several preconditioned AOR methods have been proposed to solve system of linear equations $Ax=b$, where $A \in \mathbb{R}^{n \times n}$ is a unit Z-matrix. The aim of this paper is to give a comparison result for a class of preconditioners…

Numerical Analysis · Mathematics 2014-04-09 Davod Khojasteh Salkuyeh , Mohsen Hasani , Fatemeh Panjeh Ali Beik

Inpainting based image compression approaches, especially linear and non-linear diffusion models, are an active research topic for lossy image compression. The major challenge in these compression models is to find a small set of…

Computer Vision and Pattern Recognition · Computer Science 2014-05-12 Yunjin Chen , René Ranftl , Thomas Pock

The conic bundle implementation of the spectral bundle method for large scale semidefinite programming solves in each iteration a semidefinite quadratic subproblem by an interior point approach. For larger cutting model sizes the limiting…

Optimization and Control · Mathematics 2023-08-25 Christoph Helmberg

This paper presents an iterative geometric mean decomposition (IGMD) algorithm for multiple-input-multiple-output (MIMO) wireless communications. In contrast to the existing GMD algorithms, the proposed IGMD does not require the explicit…

Information Theory · Computer Science 2013-11-05 Chiao-En Chen , Chia-Hsiang Yang

Solving optimization problems is challenging for existing digital computers and even for future quantum hardware. The practical importance of diverse problems, from healthcare to financial optimization, has driven the emergence of…

In this paper we propose to use model reduction techniques for speeding up the diagonalization-based parallel-in-time (ParaDIAG) preconditioner, for iteratively solving all-at-once systems from evolutionary PDEs. In particular, we use the…

Numerical Analysis · Mathematics 2020-12-17 Jun Liu , Zhu Wang

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

This paper investigates iterative methods for solving bi-level optimization problems where both inner and outer functions have a composite structure. We establish novel theoretical results, including the first analysis that provides…

Optimization and Control · Mathematics 2025-10-07 Shimrit Shtern , Adeolu Taiwo

Layer-wise preconditioning methods are a family of memory-efficient optimization algorithms that introduce preconditioners per axis of each layer's weight tensors. These methods have seen a recent resurgence, demonstrating impressive…

Machine Learning · Computer Science 2025-02-05 Thomas T. Zhang , Behrad Moniri , Ansh Nagwekar , Faraz Rahman , Anton Xue , Hamed Hassani , Nikolai Matni

The Shifted Boundary Method (SBM) trades some part of the burden of body-fitted meshing for increased algebraic complexity. While the resulting linear systems retain the standard $\mathcal{O}(h^{-2})$ conditioning of second-order operators,…

Numerical Analysis · Mathematics 2026-01-16 Michał Wichrowski , Ajay Ajith

Although deep learning-based personalized recommendation systems provide qualified recommendations, they strain data center resources. The main bottleneck is the embedding layer, which is highly memory-intensive due to its sparse, irregular…

Hardware Architecture · Computer Science 2025-11-26 Youngsuk Kim , Junghwan Lim , Hyuk-Jae Lee , Chae Eun Rhee

Vector extrapolation methods are widely used in large-scale simulation studies, and numerous extrapolation-based acceleration techniques have been developed to enhance the convergence of linear and nonlinear fixed-point iterative methods.…

Numerical Analysis · Mathematics 2026-02-03 Abdellatif Mouhssine

Efficient numerical solvers for partial differential equations empower science and engineering. One of the commonly employed numerical solvers is the preconditioned conjugate gradient (PCG) algorithm which can solve large systems to a given…

Numerical Analysis · Mathematics 2023-09-07 Yichen Li , Peter Yichen Chen , Tao Du , Wojciech Matusik

Particle tracing through numerical integration is a well-known approach to generating pathlines for visualization. However, for particle simulations, the computation of pathlines is expensive, since the interpolation method is complicated…

Graphics · Computer Science 2022-07-27 Haoyu Li , Tianyu Xiong , Han-Wei Shen

To precondition a large and sparse linear system, two direct methods for approximate factoring of the inverse are devised. The algorithms are fully parallelizable and appear to be more robust than the iterative methods suggested for the…

Numerical Analysis · Mathematics 2012-08-20 Mikko Byckling , Marko Huhtanen

As a generalization of Hermite interpolation problem, Birkhoff interpolation is an important subject in numerical approximation. This paper generalizes the existing Generalized Recursive Polynomial Interpolation Algorithm (GRPIA) that is…

Numerical Analysis · Mathematics 2026-01-29 Xue Jiang , Yuanhe Li , Zhe Li

In this paper, we investigate the trade-off between convergence rate and computational cost when minimizing a composite functional with proximal-gradient methods, which are popular optimisation tools in machine learning. We consider the…

Machine Learning · Computer Science 2012-10-23 Pierre Machart , Sandrine Anthoine , Luca Baldassarre

We resolve a longstanding open problem in the computational modeling of nonlinear plates by introducing a numerical method that exactly enforces the isometry constraint, namely, that the first fundamental form of the mid-surface coincides…

Numerical Analysis · Mathematics 2026-05-11 Brendan Keith , Frédéric Marazzato

Algebraic multigrid (AMG) is conventionally applied in a black-box fashion, agnostic to the underlying geometry. In this work, we propose that using geometric information -- when available -- to assist with setting up the AMG hierarchy is…

Numerical Analysis · Mathematics 2025-12-18 Songzhe Xu , Majid Rasouli , Robert M. Kirby , David Moxey , Hari Sundar

In this paper we investigate the computational aspects of some recently proposed iterative methods for approximating the canonical tight and canonical dual window of a Gabor frame (g,a,b). The iterations start with the window g while the…

Functional Analysis · Mathematics 2007-05-23 A. J. E. M. Janssen , Peter L. Soendergaard