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We consider the solution of full column-rank least squares problems by means of normal equations that are preconditioned, symmetrically or non-symmetrically, with a randomized preconditioner. With an effective preconditioner, the solutions…

Numerical Analysis · Mathematics 2025-12-29 Ilse C. F. Ipsen

In this research, to solve the large indefinite least squares problem, we firstly transform its normal equation into a sparse block three-by-three linear systems, then use GMRES method with an accelerated preconditioner to solve it. The…

Numerical Analysis · Mathematics 2025-05-26 Jun Li , Lingsheng Meng

In this note, we consider preconditioned Krylov subspace methods for discrete fluid-structure interaction problems with a nonlinear hyperelastic material model and covering a large range of flows, e.g, water, blood, and air with highly…

Numerical Analysis · Mathematics 2016-03-15 U. Langer , H. Yang

For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…

Optimization and Control · Mathematics 2021-07-30 Shengxiang Deng , Ismail Ben Ayed , Hongpeng Sun

With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of total least squares problems, i.e., solving $\min_{E,r}…

Numerical Analysis · Mathematics 2023-09-14 Eda Oktay , Erin Carson

This paper proposes a scalable binary CUR low-rank approximation algorithm that leverages parallel selection of representative rows and columns within a deterministic framework. By employing a blockwise adaptive cross approximation…

Numerical Analysis · Mathematics 2025-03-05 Bowen Su

Rational approximation appears in many contexts throughout science and engineering, playing a central role in linear systems theory, special function approximation, and many others. There are many existing methods for solving the rational…

Numerical Analysis · Mathematics 2018-12-03 Jeffrey M. Hokanson , Caleb C. Magruder

This paper discusses parGeMSLR, a C++/MPI software library for the solution of sparse systems of linear algebraic equations via preconditioned Krylov subspace methods in distributed-memory computing environments. The preconditioner…

Mathematical Software · Computer Science 2022-05-09 Tianshi Xu , Vassilis Kalantzis , Ruipeng Li , Yuanzhe Xi , Geoffrey Dillon , Yousef Saad

We introduce a novel technique for ``lifting'' dimension lower bounds for linear sketches in the real-valued setting to dimension lower bounds for linear sketches with polynomially-bounded integer entries when the input is a…

Data Structures and Algorithms · Computer Science 2025-03-26 Elena Gribelyuk , Honghao Lin , David P. Woodruff , Huacheng Yu , Samson Zhou

We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated…

Numerical Analysis · Mathematics 2018-07-17 Fabio Nobile , Raul Tempone , Soeren Wolfers

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…

Numerical Analysis · Mathematics 2019-06-26 Andrea Franceschini , Victor A. Paludetto Magri , Gianluca Mazzucco , Nicolò Spiezia , Carlo Janna

A new package for nonlinear least squares fitting is introduced in this paper. This package implements a recently developed algorithm that, for certain types of nonlinear curve fitting, reduces the number of nonlinear parameters to be…

Statistics Theory · Mathematics 2024-02-07 J. A. F. Torvisco , R. Benítez , M. R. Arias , J. Cabello Sánchez

Large-scale numerical simulations often come at the expense of daunting computations. High-Performance Computing has enhanced the process, but adapting legacy codes to leverage parallel GPU computations remains challenging. Meanwhile,…

We present a novel two-level sketching extension of the Alternating Anderson-Picard (AAP) method for accelerating fixed-point iterations in challenging single- and multi-physics simulations governed by discretized partial differential…

Numerical Analysis · Mathematics 2026-05-20 Nicolás A. Barnafi , Massimiliano Lupo Pasini

In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…

Numerical Analysis · Mathematics 2021-01-18 Luca Bergamaschi , Jacek Gondzio , Ángeles Martínez , John W. Pearson , Spyridon Pougkakiotis

We propose a randomized first order optimization algorithm Gradient Projection Iterative Sketch (GPIS) and an accelerated variant for efficiently solving large scale constrained Least Squares (LS). We provide theoretical convergence…

Optimization and Control · Mathematics 2017-07-18 Junqi Tang , Mohammad Golbabaee , Mike Davies

We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element…

Numerical Analysis · Mathematics 2023-10-26 Fatemeh P. A. Beik , Michele Benzi

We consider the solution of large stiff systems of ordinary differential equations with explicit exponential Runge--Kutta integrators. These problems arise from semi-discretized semi-linear parabolic partial differential equations on…

Numerical Analysis · Mathematics 2023-08-24 Kai Bergermann , Martin Stoll

Peer review systems such as conference paper review often suffer from the issue of miscalibration. Previous works on peer review calibration usually only use the ordinal information or assume simplistic reviewer scoring functions such as…

Machine Learning · Computer Science 2021-10-26 Sijun Tan , Jibang Wu , Xiaohui Bei , Haifeng Xu

The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-12-29 Poorna Banerjee Dasgupta