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Search · four archives
29 papers · ranked by Valyu relevance
Muhammad Usman, Javed Iqbal, Alamgir Khan, Ikram Ullah + 3 more
'Jehad Alzabut' 'Hisham Mohammad Alkhawar'] This study introduces an advanced iterative technique designed to solve nonlinear equations with simple roots efficiently. The newly developed algorithm achieves an impressive convergence order of sixteen, utilizing only five functional evaluations per iteration. By…
Zakaria Kasmi, Abdelmoumen Norrdine, Jochen Schiller, Mesut Güneş + 2 more
'Christoph Motzko' 'Raffaele Bruno'] We developped an open source library called RcdMathLib for solving multivariate linear and nonlinear systems. RcdMathLib supports on-the-fly computing on low-cost and resource-constrained devices, e.g., microcontrollers. The decentralized processing is a step towards ubiquitous…
Fayyaz Ahmad, Domingo Garcı́a-Senz
In this article, we report on sixth-order and seventh-order iterative methods for solving nonlinear equations. In particular sixth-order derivative-based and derivative-free iterative families are constructed in such a way that they comprise a wide class of sixth-order methods which were developed in the past years.…
Mahdi Shamsi, Mahmoud Ghandi, Farokh Marvasti
Iterative methods have led to better understanding and solving problems such as missing sampling, deconvolution, inverse systems, impulsive and Salt and Pepper noise removal problems. However, the challenges such as the speed of convergence and or the accuracy of the answer still remain. In order to improve the…
Srinivasarao Thota, P. Shanmugasundaram
Objectives This paper proposes three iterative methods of order three, six and seven respectively for solving non-linear equations using the modified homotopy perturbation technique coupled with system of equations. This paper also discusses the analysis of convergence of the proposed iterative methods. Results Several…
Srinivasarao Thota, Mohamed M. Awad, P. Shanmugasundaram, Laxmi Rathour
'Laxmi Rathour'] Objective In this paper, we develop a new root-finding algorithm to solve the given non-linear equations. The proposed root-finding algorithm is based on the exponential method. This algorithm is derivative-free and converges fast. Results Several numerical examples are presented to illustrate and…
Gonglin Yuan, Xiabin Duan, Wenjie Liu, Xiaoliang Wang + 3 more
'Zhou Sheng' 'Yongtang Shi'] Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains…
Peter Brune, Matthew G. Knepley, Barry Smith, Xuemin Tu
Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for nonlinear algebraic systems, where nonlinear composition of different nonlinear solvers may…
Antonio Gómez‐Expósito
—This article generalizes a recently introduced procedure to solve nonlinear systems of equations, radically departing from the conventional Newton-Raphson scheme. The original nonlinear system is first unfolded into three simpler components: 1) an underdetermined linear system; 2) a one-to-one nonlinear mapping with…
Adrian Przybylski, Björn Thiel, Jan Keller-Findeisen, Bernd Stock + 1 more
We present a general purpose, open-source software library for estimation of non-linear parameters by the Levenberg-Marquardt algorithm. The software, Gpufit, runs on a Graphics Processing Unit (GPU) and executes computations in parallel, resulting in a significant gain in performance. We measured a speed increase of…
Marta M. Betcke, Heinrich Voss
In this work we present a new restart technique for iterative projection methods for nonlinear eigenvalue problems admitting minmax characterization of their eigenvalues. Our technique makes use of the minmax induced local enumeration of the eigenvalues in the inner iteration. In contrast to global numbering which…
Guy Gilboa
In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and 39 more. The canonical eigenproblem we solve is T(u) = λu, where T : R n → R n is some bounded nonlinear operator.…
Anna Löschberger, Yauheni Novikau, Ralf Netz, Marie-Christine Spindler + 4 more
Three-dimensional (3D) multicolor super-resolution imaging in the 50-100 nm range in fixed and living cells remains challenging. We extend the resolution of structured illumination microscopy (SIM) by an improved nonlinear iterative reconstruction algorithm that enables 3D multicolor imaging with improved…
Masoud Ahookhosh, Susan Ghaderi
Monotonicity and nonmonotonicity play a key role in studying the global convergence and the efficiency of iterative schemes employed in the field of nonlinear optimization, where globally convergent and computationally efficient schemes are explored. This paper addresses some features of descent schemes and the…
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open- source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
AKHIL SHAJAN, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open-source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
Kevin Robben, Christopher Cheatum
We report a comprehensive study of the efficacy of least-squares fitting of multidimensional spectra to generalized Kubo lineshape models and introduce a novel least-squares fitting metric, termed the Scale Invariant Gradient Norm (SIGN), that enables a highly reliable and versatile algorithm. The precision of…
Fabian Fröhlich, Peter K. Sorger
Ordinary differential equation (ODE) models are widely used to describe biochemical processes, since they effectively represent mass action kinetics. Optimization-based calibration of ODE models on experimental data can be challenging, even for low-dimensional problems. However, reliable model calibration is a…
Alejandro Apolinar-Fernández, Jorge Barrasa-Fano, Hans Van Oosterwyck, José A. Sanz-Herrera
Accurate characterization of cellular tractions is crucial for understanding cell-extracellular matrix (ECM) mechanical interactions and their implications in pathology-related situations, yet their direct measurement in experimental setups remains challenging. Traction Force Microscopy (TFM) has emerged as a key…
Negin Bagherpour, Nezam Mahdavi‐Amiri
Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute a symmetric and positive definite solution. Here, we propose new iterative…
Philku Lee, Tai Wan Kim, Seongjai Kim
Elliptic obstacle problems are formulated to find either superharmonic solutions or minimal surfaces that lie on or over the obstacles, by incorporating inequality constraints. In order to solve such problems effectively using finite difference (FD) methods, the article investigates simple iterative algorithms based on…
Abbas Kazemipour, Behtash Babadi, Min Wu, Kaspar Podgorski + 1 more
We consider the problem of optimizing general convex objective functions with nonnegativity constraints. Using the Karush-Kuhn-Tucker (KKT) conditions for the nonnegativity constraints we will derive fast multiplicative update rules for several problems of interest in signal processing, including non-negative…
Authors not listed
Inverse problems, where we seek the values of inputs to a model that lead to a desired set of outputs, are a challenges subset of problems in science and engineering. In this work we demonstrate the use of two generative AI methods to solve inverse problems. We compare this approach to two more conventional approaches…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Philipp Flotho, David Thinnes, Bernd Kuhn, Christopher J. Roome + 2 more
In the context of signal analysis and pattern matching, alignment of 1D signals for the comparison of signal morphologies is an important problem. For image processing and computer vision, 2D optical flow (OF) methods find wide application for motion analysis and image registration and variational OF methods have been…
Lippl Samuel, Peters Benjamin, Kriegeskorte Nikolaus
Recent work has suggested that feedforward residual neural networks (ResNets) approximate iterative recurrent computations. Iterative computations are useful in many domains, so they might provide good solutions for neural networks to learn. Here we quantify the degree to which ResNets learn iterative solutions and…
Authors not listed
Rapid and robust simulation of chemical processes is critical to conduct process design, optimization, techno-economic analysis, and sustainability analysis. Yet, efficiently solving simulation models remains a challenge due to the highly coupled and nonlinear nature of the underlying algebraic equations that capture…
Authors not listed
Solving optimization problems, especially for nonlinear and constrained systems, is a challenge. Decades of specialized algorithms have been developed for general and special cases of root finding, minimization (including constraints), for parameter estimation, and mapping connected spaces. These approaches typically…