Article
Mathematics
Yongxin Yuan, Lei Zhou, Jinghua Chen
Summary: The model updating for damped gyroscopic systems can be formulated as an inverse quadratic eigenvalue problem (IQEP) and an optimal approximation problem (OAP). The IQEP involves finding a given value for p, where...
LINEAR & MULTILINEAR ALGEBRA
(2021)
Article
Mathematics, Applied
Jiao Xu, Yinlan Chen
Summary: In this paper, we first consider the inverse palindromic eigenvalue problem (IPEP) and the best approximation problem (BAP). By partitioning the matrix Lambda and using QR-decomposition, the general solution of Problem IPEP is derived, and it is shown that the best approximation solution A is unique.
Article
Mathematics
T. L. M. Luna, A. N. Carvalho
Summary: In this paper, we investigate the existence of solutions to a one-dimensional eigenvalue problem with given boundary conditions. We provide a complete description of the solutions, which may be uncountable. Our method of proof involves analyzing the phase diagram associated with the equation and refining previous results on the regularity of solutions. The importance of this study lies in its contribution to a fuller understanding of the problem, as existing results are limited to specific cases.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Hongjia Chen, Lei Du, Zongqi Cao
Summary: This paper analyzes the backward error of approximate eigenpairs computed by two balancing strategies for heavily damped QEP, and finds that the backward error of approximate eigenpairs by linearizing-balancing is smaller than that by balancing-linearizing under relatively mild conditions. Numerical experiments demonstrate the advantages of linearizing-balancing.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
M. Bueno, J. Perez, S. Rogers
Summary: This paper explores the solution to even degree matrix polynomials and proposes two block-symmetric linearization methods that overcome the issue of backward error in the traditional approach.
Article
Mathematics
Yongxin Yuan
Summary: This paper addresses the problem of optimal approximation for a given matrix pencil under spectral and symmetric constraints, and establishes an explicit formulation for the solution using constrained optimization theory and matrix derivatives. The proposed method's efficiency and accuracy is numerically verified through a simple five-degree-of-freedom system.
QUAESTIONES MATHEMATICAE
(2021)
Article
Engineering, Multidisciplinary
Suman Rakshit, Biswa Nath Datta
Summary: The paper investigates the symmetric band partial quadratic inverse eigenvalue problem, proposing a novel method based on matrix-vectorization and Kronecker product of matrices to solve the problem. It presents explicit expressions for general solutions and demonstrates the applicability and practical usefulness of the proposed method through numerical experiments on a spring mass problem.
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
(2021)
Article
Operations Research & Management Science
Baohua Huang, Changpeng Ma, Yajun Xie
Summary: This paper presents a nonlinear conjugate gradient method for finding the least squares solution of the quadratic inverse eigenvalue problem under a prescribed submatrix constraint. The convergence analysis and numerical examples demonstrate the efficiency of the proposed method.
PACIFIC JOURNAL OF OPTIMIZATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Antigoni Kleanthous, Timo Betcke, David P. Hewett, Paul Escapil-Inchauspe, Carlos Jerez-Hanckes, Anthony J. Baran
Summary: We investigate various techniques to accelerate Calderon preconditioning in the context of boundary integral equation methods for electromagnetic transmission problems. By employing barycentric meshes only for the preconditioner and discarding non-essential boundary integral operators, and by using a lower-quality H-matrix assembly routine with the novel approach of discarding far-field interactions, we achieve significant reductions in computational cost. Experimental results on scattering by multiple dielectric particles demonstrate that our accelerated implementation can significantly reduce memory cost and computation time compared to a non-accelerated implementation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Chemistry, Physical
Carlos Damian Rodriguez-Fernandez, Luis M. Varela, Christian Schroder, Elena Lopez Lago
Summary: This work evaluates the role of charge delocalization in the non-linear optical response of ionic liquids. The first and second hyperpolarizabilities for the non-linear processes of second harmonic generation (SHG) and electro-optical Kerr-Effect (EOKE) were estimated using density functional theory calculations. The results show that both charge delocalization and molecular geometry are crucial factors in governing the hyperpolarizabilities of ionic liquids.
JOURNAL OF MOLECULAR LIQUIDS
(2022)
Article
Mathematics, Applied
Timo Betcke, Michal Bosy, Erik Burman
Summary: In this paper, a hybrid method for FEM-BEM coupling is discussed. The coupling from both sides uses a Nitsche-type approach to couple to the trace variable. This leads to a formulation that is robust and flexible, and can easily be combined with other hybrid methods.
NUMERICAL ALGORITHMS
(2022)
Article
Optics
Christian Brunner, Andreas Duensing, Christian Schroeder, Michael Mittermair, Vladimir Golkov, Maximilian Pollanka, Daniel Cremers, Reinhard Kienberger
Summary: In this study, deep neural networks are applied to solve the challenge of information extraction from spectrograms recorded with the attosecond streak camera in time-resolved photoelectron spectroscopy. Extensive benchmarking on simulated data shows that the deep neural networks exhibit competitive retrieval quality and superior tolerance against noisy data conditions.
Article
Mathematics, Applied
Zvonimir Bujanovic, Daniel Kressner, Christian Schroeder
Summary: The study focuses on computing a more accurate Schur decomposition from a given approximate Schur decomposition, and proposes a Newton-like algorithm that exhibits local quadratic convergence on matrices with mutually distinct eigenvalues.
NUMERICAL ALGORITHMS
(2023)
Article
Engineering, Electrical & Electronic
Ignacia Fierro-Piccardo, Timo Betcke
Summary: The electric field integral equation (EFIE) is a widely used tool for solving electromagnetic scattering problems. However, the development of efficient and easy-to-implement preconditioners for the EFIE is an ongoing research area. In recent years, operator preconditioning approaches have gained popularity, and the use of approximate local magnetic-to-electric (MtE) operators has shown promise in reducing computational costs. This article presents the implementation and numerical comparisons of these approximate MtE operators as preconditioners for the EFIE, highlighting their effectiveness.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2023)
Article
Chemistry, Physical
Philipp Honegger, Othmar Steinhauser, Christian Schroeder
Summary: Different spectroscopy types reveal different aspects of molecular processes in soft matter, with collective observables providing insights into intermolecular correlations. This perspective focuses on the interpretation of dielectric relaxation spectroscopy (DRS) utilizing computational spectroscopy. It discusses the history and recent advances of DRS in biomolecular hydration and nanoconfinement, while also providing guidance on utilizing collective spectroscopy types to understand soft matter phenomena.
JOURNAL OF PHYSICAL CHEMISTRY LETTERS
(2023)
Article
Mathematics, Applied
Massimiliano Fasi, Nicholas J. Higham, Florent Lopez, Theo Mary, Mantas Mikaitis
Summary: This paper investigates the use of multiword arithmetic to improve the performance-accuracy tradeoff of matrix multiplication with mixed precision block fused multiply--add (FMA) hardware, focusing on NVIDIA GPUs' tensor cores. The authors develop an error analysis of multiword matrix multiplication and implement several algorithms using double-fp16 arithmetic. However, they find that double-fp16 is less accurate than fp32 arithmetic, despite satisfying the same worst-case error bound. By using probabilistic error analysis, they identify the rounding mode used by the NVIDIA tensor cores as the likely cause and propose a parameterized blocked summation algorithm to alleviate the problem and improve the performance-accuracy tradeoff.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
Article
Computer Science, Software Engineering
Patrick Amestoy, Alfredo Buttari, Nicholas J. Higham, Jean-Yves L'excellent, Theo Mary, Bastien Vieuble
Summary: The speed and accuracy of the standard LU factorization-based solution process for linear systems can be improved by using mixed-precision iterative refinement. This study explores the potential of mixed-precision iterative refinement for enhancing methods for sparse systems based on approximate sparse factorizations. A new error analysis is developed for LU- and GMRES-based iterative refinement, considering the approximation methods used by modern sparse solvers. Performance analysis is conducted on different algorithms, based on selected iterative refinement variants and approximate sparse factorizations. The results show that mixed-precision iterative refinement combined with approximate sparse factorization can significantly reduce both time and memory consumption.
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
(2023)
Article
Geochemistry & Geophysics
Bin Zhao, Peng Yao, Xuchen Wang, Thomas S. Bianchi, Michael R. Shields, Christian Schroder, Zhigang Yu
Summary: The aim of this study was to investigate the changes in the bound form of reactive iron (Fe-R) and organic carbon (OC) from estuarine suspended particulate matter (SPM) to coastal sediments. The results showed that the percentage of OC bound to Fe-R remained stable in SPM and mobile-mud sediments, indicating that binding with Fe-R is a potential long-term protection mechanism for terrestrial OC. Fe-R was mainly associated with pre-aged soil OC of terrestrial plant origin.
GEOCHIMICA ET COSMOCHIMICA ACTA
(2023)
Article
Mathematics, Applied
Massimiliano Fasi, Nicholas J. Higham, Xiaobo Liu
Summary: This paper investigates the problem of computing the square root of a perturbation of the scaled identity matrix and proposes a new formula and Newton iteration method to calculate the result more efficiently.
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
(2023)
Article
Chemistry, Multidisciplinary
Florian Joerg, Marcus Wieder, Christian Schroeder
Summary: Protex is an open-source program that allows for proton exchanges of solvent molecules during molecular dynamics simulations, enhancing traditional simulations by permitting bond breaking or formation. It provides an easy-to-use interface for defining multiple proton sites for (de-)protonation using a single topology approach. Protex has been successfully applied to a protic ionic liquid system and compared to simulations without proton exchange, showing accurate calculation of transport properties.
FRONTIERS IN CHEMISTRY
(2023)
Article
Mathematics, Applied
Michael P. Connolly, Nicholas J. Higham
Summary: This research proves that the normwise backward error bound for Householder QR factorization can be replaced by a probabilistic bound, which is applicable to various numerical linear algebra algorithms. Numerical experiments further validate this conclusion and show that the probabilistic bounds provide a better indicator of the actual backward errors and their rate of growth compared to worst-case bounds.
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
(2023)
Article
Chemistry, Physical
Andras Szabadi, Aleksandar Doknic, Jonathan Netsch, Adam Mark Palvoegyi, Othmar Steinhauser, Christian Schroeder
Summary: We use polarizable molecular dynamics simulations to reproduce the infrared spectra of several ionic liquid cations and anions in the gas phase. Our results show that polarizable force fields provide a reasonable compromise between computational effort and accuracy for investigating IR spectra when treating the transition from gas to liquid phase carefully. The liquid phase not only changes the electrostatic environment of the molecules, but also introduces friction and intermolecular interactions, altering the IR spectrum significantly. Additionally, we tested the application of machine learning potentials in reproducing IR spectra but found that the main focus of this work is to improve the quality of polarizable force fields concerning vibrations rather than predicting IR spectra.
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Sven Hammarling, Nicholas J. Higham
Summary: This article pays tribute to Jack Dongarra, the recipient of the 2021 ACM Turing Award, and focuses on his contributions to numerical linear algebra, specifically the development of algorithms and software for solving linear algebra problems reliably and efficiently. The article discusses various software projects initiated by Jack, from the BLAS and LINPACK to recent ones like SLATE, as well as highlighting some of his algorithmic contributions.
COMPUTING IN SCIENCE & ENGINEERING
(2022)
