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Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…

Nuclear Theory · Physics 2023-04-05 Caleb Hicks , Dean Lee

A general asynchronous alternating iterative model is designed, for which convergence is theoretically ensured both under classical spectral radius bound and, then, for a classical class of matrix splittings for $\mathsf H$-matrices. The…

Numerical Analysis · Mathematics 2023-12-29 Guillaume Gbikpi-Benissan , Qinmeng Zou , Frédéric Magoulès

We develop and analyze the Generalized Multiplicative Gradient (GMG) method for solving a class of convex optimization problems over symmetric cones, where the objective function does not have Lipschitz gradient over the feasible region.…

Optimization and Control · Mathematics 2026-03-06 Renbo Zhao

In this paper, we reconsider two new iterative methods for solving absolute value equations (AVE), which is proposed by Ali and Pan (Jpn. J. Ind. Appl. Math. 40: 303--314, 2023). Convergence results of the two iterative schemes and new…

Numerical Analysis · Mathematics 2024-12-17 Jiayu Liu , Tingting Luo , Cairong Chen

Recently Ahmadi et al. (2021) and Tagliaferro (2022) proposed some iterative methods for the numerical solution of linear systems which, under the classical hypothesis of strict diagonal dominance, typically converge faster than the Jacobi…

Numerical Analysis · Mathematics 2024-04-11 Paolo Novati , Fulvio Tagliaferro , Marino Zennaro

The Conjugate Gradient method (CGM) is known to be the fastest generic iterative method for solving linear systems with symmetric sign definite matrices. In this paper, we modify this method so that it could find fundamental solitary waves…

Pattern Formation and Solitons · Physics 2015-05-13 Taras I. Lakoba

The focus of this work is on an alternative implementation of the iterative ensemble smoother (iES). We show that iteration formulae similar to those used in \cite{chen2013-levenberg,emerick2012ensemble} can be derived by adopting a…

Data Analysis, Statistics and Probability · Physics 2016-02-11 Xiaodong Luo , Andreas S. Stordal , Rolf J. Lorentzen , Geir Nævdal

We introduce an iterative method named GPMR for solving 2x2 block unsymmetric linear systems. GPMR is based on a new process that reduces simultaneously two rectangular matrices to upper Hessenberg form and that is closely related to the…

Numerical Analysis · Mathematics 2021-11-16 Alexis Montoison , Dominique Orban

A new, very general, robust procedure for combining estimators in metric spaces is introduced GROS. The method is reminiscent of the well-known median of means, as described in \cite{devroye2016sub}. Initially, the sample is divided into…

Statistics Theory · Mathematics 2024-02-26 Alejandro Cholaquidis , Emilien Joly , Leonardo Moreno

With the growth of data, it is more important than ever to develop an efficient and robust method for solving the consistent matrix equation AXB=C. The randomized Kaczmarz (RK) method has received a lot of attention because of its…

Numerical Analysis · Mathematics 2025-07-21 Nian-Ci Wu , Yang Zhou , Zhaolu Tian

Randomized Kaczmarz (RK), Motzkin Method (MM) and Sampling Kaczmarz Motzkin (SKM) algorithms are commonly used iterative techniques for solving a system of linear inequalities (i.e., $Ax \leq b$). As linear systems of equations represent a…

Optimization and Control · Mathematics 2022-08-16 Md Sarowar Morshed , Md Saiful Islam , Md. Noor-E-Alam

We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…

Machine Learning · Computer Science 2022-04-19 Gideon Dresdner , Maria-Luiza Vladarean , Gunnar Rätsch , Francesco Locatello , Volkan Cevher , Alp Yurtsever

Graph matching aims at finding the vertex correspondence between two unlabeled graphs that maximizes the total edge weight correlation. This amounts to solving a computationally intractable quadratic assignment problem. In this paper we…

Machine Learning · Statistics 2019-07-23 Zhou Fan , Cheng Mao , Yihong Wu , Jiaming Xu

The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…

Numerical Analysis · Mathematics 2016-08-23 Debasisha Mishra

This paper proposes Inverse Gram Matrix (IGM) methods to prioritize the Pairwise Reciprocal Matrix (PRM) in the Analytic Hierarchy Process. The IGM methods include Pseudo-IGM, Normalized-IGM, and Lagrange-IGM. Interestingly, the proposed…

Optimization and Control · Mathematics 2024-01-03 Kevin Kam Fung Yuen

Greville's method has been utilized in (Broad Learn-ing System) BLS to propose an effective and efficient incremental learning system without retraining the whole network from the beginning. For a column-partitioned matrix where the second…

Numerical Analysis · Mathematics 2022-10-28 Hufei Zhu

A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and $\varphi$ matrix function evaluations. The approach is intended for iterative methods computing the matrix-vector products with…

Numerical Analysis · Mathematics 2024-04-23 Mike A. Botchev

In this paper, two efficient iterative algorithms based on the simpler GMRES method are proposed for solving shifted linear systems. To make full use of the shifted structure, the proposed algorithms utilizing the deflated restarting…

Numerical Analysis · Mathematics 2021-07-26 Hong-Xiu Zhong , Xian-Ming Gu

In this paper we present computational experiments with the Markov Chain Monte Carlo Matrix Inversion ($(\text{MC})^2\text{MI}$) on several accelerator architectures and investigate their impact on performance and scalability of the method.…

Numerical Analysis · Mathematics 2024-09-06 Anton Lebedev , Vassil Alexandrov

Although many techniques have been applied to matrix factorization (MF), they may not fully exploit the feature structure. In this paper, we incorporate the grouping effect into MF and propose a novel method called Robust Matrix…

Machine Learning · Computer Science 2021-07-09 Haiyan Jiang , Shuyu Li , Luwei Zhang , Haoyi Xiong , Dejing Dou