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The derivative-free projection method (DFPM) is an efficient algorithm for solving monotone nonlinear equations. As problems grow larger, there is a strong demand for speeding up the convergence of DFPM. This paper considers the application…

Optimization and Control · Mathematics 2026-01-23 Jiachen Jin , Hongxia Wang , Kangkang Deng

We present a convergence theory for Anderson acceleration (AA) applied to perturbed Newton methods (pNMs) for computing roots of nonlinear problems. Two important special cases are the classical Newton method and the Levenberg-Marquardt…

Numerical Analysis · Mathematics 2025-12-03 Matt Dallas

In this note we take a new look at the local convergence of alternating optimization methods for low-rank matrices and tensors. Our abstract interpretation as sequential optimization on moving subspaces yields insightful reformulations of…

Numerical Analysis · Mathematics 2019-01-14 Ivan Oseledets , Maxim Rakhuba , André Uschmajew

The paper focuses on the development of numerical methods for the compressible Euler equations. It is well-known that if the Mach number is small, the system becomes stiff and hence explicit schemes suffer from severe time-step…

Numerical Analysis · Mathematics 2026-04-30 Alina Chertock , Smadar Karni , Alexander Kurganov , Lorenzo Micalizzi

This paper proposes an accelerated version of Feasible Sequential Linear Programming (FSLP): the AA($d$)-FSLP algorithm. FSLP preserves feasibility in all intermediate iterates by means of an iterative update strategy which is based on…

Optimization and Control · Mathematics 2024-07-08 David Kiessling , Pieter Pas , Alejandro Astudillo , Panagiotis Patrinos , Jan Swevers

This paper investigates the use of fixed-point Anderson acceleration method (AA) to a recently proposed hierarchical control framework. Due to its model-free property, the AA-based resulting hierarchical framework becomes more generic since…

Systems and Control · Electrical Eng. & Systems 2021-12-09 Xuan-Huy Pham , Mazen Alamir , François Bonne , Patrick Bonnay

We propose a new stochastic dual coordinate ascent technique that can be applied to a wide range of regularized learning problems. Our method is based on Alternating Direction Multiplier Method (ADMM) to deal with complex regularization…

Machine Learning · Statistics 2013-11-05 Taiji Suzuki

This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…

Optimization and Control · Mathematics 2021-08-17 Nicolas Lepage-Saucier

Multilinear systems play an important role in scientific calculations of practical problems. In this paper, we consider a tensor splitting method with a relaxed Anderson acceleration for solving multilinear systems. The new method preserves…

Numerical Analysis · Mathematics 2024-10-18 Dongdong Liu Ting Hua nd Xifu Liu

We present the Alternating Anderson-Richardson (AAR) method: an efficient and scalable alternative to preconditioned Krylov solvers for the solution of large, sparse linear systems on high performance computing platforms. Specifically, we…

Numerical Analysis · Mathematics 2018-04-12 Phanish Suryanarayana , Phanisri P. Pratapa , John E. Pask

The Newton's method for solving stationary Navier-Stokes equations (NSE) is known to convergent fast, however, may fail due to a bad initial guess. This work presents a simple-to-implement nonlinear preconditioning of Newton's iteration,…

Numerical Analysis · Mathematics 2025-08-01 Muhammad Mohebujjaman , Mengying Xiao , Cheng Zhang

We present a novel framework, namely AADMM, for acceleration of linearized alternating direction method of multipliers (ADMM). The basic idea of AADMM is to incorporate a multi-step acceleration scheme into linearized ADMM. We demonstrate…

Optimization and Control · Mathematics 2014-02-13 Yuyuan Ouyang , Yunmei Chen , Guanghui Lan , Eduardo Pasiliao

We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose…

Numerical Analysis · Mathematics 2023-04-25 Sergey A. Matveev , Stanislav Budzinskiy

The alternating minimization (AM) method is a fundamental method for minimizing convex functions whose variable consists of two blocks. How to efficiently solve each subproblems when applying the AM method is the most concerned task. In…

Optimization and Control · Mathematics 2015-01-16 Hui Zhang , Lizhi Cheng

A two-step method for solving planar Laplace problems via rational approximation is introduced. First complex rational approximations to the boundary data are determined by AAA approximation, either globally or locally near each corner or…

Numerical Analysis · Mathematics 2021-07-06 Stefano Costa , Lloyd N. Trefethen

This paper considers an enhancement of the classical iterated penalty Picard (IPP) method for the incompressible Navier-Stokes equations, where we restrict our attention to $O(1)$ penalty parameter, and Anderson acceleration (AA) is used to…

Numerical Analysis · Mathematics 2021-10-13 Leo G. Rebholz , Duygu Vargun , Mengying Xiao

We present a stationary iteration method, namely Alternating Symmetric positive definite and Scaled symmetric positive semidefinite Splitting (ASSS), for solving the system of linear equations obtained by using finite element discretization…

Numerical Analysis · Mathematics 2021-09-06 Davod Khojasteh Salkuyeh

The Method of Alternating Projections (MAP), a classical algorithm for solving feasibility prob- lems, has recently been intensely studied for nonconvex sets. However, intrinsically available are only local convergence results: convergence…

Optimization and Control · Mathematics 2013-05-21 Heinz H. Bauschke , Hung M. Phan , Xianfu Wang

A pervasive approach in scientific computing is to express the solution to a given problem as the limit of a sequence of vectors or other mathematical objects. In many situations these sequences are generated by slowly converging iterative…

Numerical Analysis · Mathematics 2025-07-17 Yousef Saad

Rational approximation is a powerful tool to obtain accurate surrogates for nonlinear functions that are easy to evaluate and linearize. The interpolatory adaptive Antoulas--Anderson (AAA) method is one approach to construct such…

Numerical Analysis · Mathematics 2024-06-27 Stefan Güttel , Daniel Kressner , Bart Vandereycken