26 papers · ranked by Valyu relevance
Dominic Kealoha, Fabiola Rojas, Xingjie Li
Iterative Methods Authors: ['Dominic Kealoha' 'Fabiola Rojas' 'Xingjie Li'] Iterative methods such as Jacobi, Gauss-Seidel, and Successive Over-Relaxation (SOR) are fundamental tools in solving large systems of linear equations across various scientific fields, particularly in the field of data science which has become…
Zhuande Wang, Chuansheng Yang, Yubo Yuan
In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is…
Olivia Choudhury, Ankush Chakrabarty, Scott J. Emrich
Second-generation sequencing techniques generate short reads that can result in fragmented genome assemblies. Third-generation sequencing platforms mitigate this limitation by producing longer reads that span across complex and repetitive regions. Currently, the usefulness of such long reads is limited, however…
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…
Majid Jahani, Naga V. C. Gudapati, Chenxin Ma, Rachael Tappenden + 1 more
'Martin Takáč'] Abstract In this work we introduce the concept of an Underestimate Sequence (UES), which is a natural extension of Nesterov's estimate sequence [16]. Our definition of a UES utilizes three sequences, one of which is a lower bound (or under-estimator) of the objective function. The question of how to…
Srinivasarao Thota, Vivek Kumar Srivastav
Objectives The present paper describes a new algorithm to find a root of non-linear transcendental equations. It is found that Regula-Falsi method always gives guaranteed result but slow convergence. However, Newton-Raphson method does not give guaranteed result but faster than Regula-Falsi method. Therefore, the…
Bilal Khurshid, Shahid Maqsood, Yahya Khurshid, Khawar Naeem + 1 more
This study investigates the no-wait flow shop scheduling problem and proposes a hybrid (HES-IG) algorithm that utilizes makespan as the objective function. To address the complexity of this NP-hard problem, the HES-IG algorithm combines evolution strategies (ES) and iterated greedy (IG) algorithm, as hybridizing…
Bin Zhao, John A. Lees, Hongjin Wu, Chao Yang + 1 more
Bacterial genome data are accumulating at an unprecedented speed due the routine use of sequencing in clinical diagnoses, public health surveillance and population genetics studies. Genealogical reconstruction is fundamental to many of these uses, however, inferring genealogy from large-scale genome datasets quickly…
F. Soleymani, Predrag S. Stanimirović
A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the…
Authors not listed
Identifying synthesis routes from knowledge graphs poses challenges beyond retrosynthesis, including path–finding artifacts and data issues. We introduce “SynGPS”, a novel algorithm that overcomes these limitations by identifying viable routes even with common artifacts. SynGPS can resolve nonsensical cycles…
Ireneusz Gościniak, Krzysztof Gdawiec
There is a huge group of algorithms described in the literature that iteratively find solutions of a given equation. Most of them require tuning. The article presents root-finding algorithms that are based on the Newton-Raphson method which iteratively finds the solutions, and require tuning. The modification of the…
Cliff C. Kerr, Salvador Dura-Bernal, Tomasz G. Smolinski, George L. Chadderdon + 2 more
'George L. Chadderdon' 'David P. Wilson' 'Lars Kaderali'] When standard optimization methods fail to find a satisfactory solution for a parameter fitting problem, a tempting recourse is to adjust parameters manually. While tedious, this approach can be surprisingly powerful in terms of achieving optimal or near-optimal…
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…
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…
Pier Paolo Poier, Louis Lagardère, Jean-Philip Piquemal
We propose a new strategy to solve the Tkatchenko-Scheffler Many-Body Dispersion (MBD) model’s equations. Our approach overcomes the original O(N**3) computational complexity that limits its applicability to large molecular systems within thecontext of O(N) Density Functional Theory (DFT). First, in order to generate…
Hideaki Iiduka
The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is considered. The use of proximal point algorithms that use the proximity operators…
Kazunori D Yamada
In the deep learning era, a gradient descent method is the most common method to optimize parameters of neural networks. Among various mathematical optimization methods, a gradient descent method is the most naive method. Although controlling a learning rate of the method is necessary for quick convergence, the…
Gengsheng L Zeng, Edward V DiBella
Magnetic resonance imaging (MRI) using under-sampled k-space data is a common method to shorten the imaging time. Iterative Bayesian algorithms are usually used for its image reconstruction. This paper compares an iterative Bayesian image reconstruction method that uses both spatial and temporal constraints and a…
Henrik Barthels
[_page_0_Picture_2.jpeg]: Master's Thesis Henrik Barthels, B.Sc. Supervised by Prof. Paolo Bientinesi, Ph.D. Prof. Georg May, Ph.D. This is a revised edition of the author's thesis. Corrections of typographical errors and clarifications of some passages. [' \nFigure 1: Figure 1\n \n \nFigure 1: Figure 1\n \nFigure 1\n…
Yann Garniron, Thomas Applencourt, Kevin Gasperich, Anouar Benali + 15 more
Quantum Package is an open-source programming environment for quantum chemistry specially designed for wave function methods. Its main goal is the development of determinant-driven selected configuration interaction (sCI) methods and multi-reference second-order perturbation theory (PT2). The determinant-driven…
Minati De, Subhas C. Nandy, Sasanka Roy
Prune-and-search is an important paradigm for solving many important geometric problems. We show that the general prune-andsearch technique can be implemented where the objects are given in read-only memory. As examples we consider convex-hull in 2D, and linear programming in 2D and 3D. For the convex-hull problem…
Authors not listed
This paper presents a simplified model of iterative compound optimization in drug/agrochemical discovery. Compounds are represented as binary strings, with project evolution simulated through random bit changes. The model reproduces key statistical features of real projects, including activity distributions and…
A. Emre Cetin
A novel integer value-sorting technique is proposed replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. It requires only constant amount of additional memory. The technique is inspired from one of the ordinal theories of "serial order in behavior" and explained by the…
Peter L. Bartlett, Chris Junchi Li, Jingfeng Wu, Bin Yu
In the field of optimization, developing accelerated methods for solving minimax and fixed-point problems remains a fundamental challenge. This paper presents a novel family of dual accelerated algorithms that achieve optimal convergence rates for both minimax and fixed-point problems. By exploring new anchoring…
Mikko Rautiainen, Veli Mäkinen, Tobias Marschall
Graphs are commonly used to represent sets of sequences. Either edges or nodes can be labeled by sequences, so that each path in the graph spells a concatenated sequence. Examples include graphs to represent genome assemblies, such as string graphs and de Bruijn graphs, and graphs to represent a pan-genome and hence…
Ricardo H. C. Takahashi, Ivo Fagundes David de Oliveira
We find a searching method on ordered lists that surprisingly outperforms binary searching with respect to average query complexity while retaining minmax optimality. The method is shown to require O(log2 log2 n) queries on average while never exceeding dlog2 ne queries in the worst case, i.e. the minmax bound of…