Applied Numerical Mathematics最新文献_第7页

Fast alternating fitting methods for trigonometric curves for large data sets 大型数据集三角曲线的快速交替拟合方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.01.001

Alessandro Buccini , Fei Chen , Omar De la Cruz Cabrera , Lothar Reichel

{"title":"Fast alternating fitting methods for trigonometric curves for large data sets","authors":"Alessandro Buccini , Fei Chen , Omar De la Cruz Cabrera , Lothar Reichel","doi":"10.1016/j.apnum.2024.01.001","DOIUrl":"10.1016/j.apnum.2024.01.001","url":null,"abstract":"<div><div>This paper discusses and develops new methods for fitting trigonometric curves, such as circles, ellipses, and dumbbells, to data points in the plane. Available methods for fitting circles or ellipses are very sensitive to outliers in the data, and are time consuming when the number of data points is large. The present paper focuses on curve fitting methods that are attractive to use when the number of data points is large. We propose a direct method for fitting circles, and two iterative methods for fitting ellipses and dumbbell curves based on trigonometric polynomials. These methods efficiently minimize the sum of the squared geometric distances between the given data points and the fitted curves. In particular, we are interested in detecting the general shape of an object such as a galaxy or a nebula. Certain nebulae, for instance, the one shown in the experiment section, have a dumbbell shape. Methods for fitting dumbbell curves have not been discussed in the literature. The methods developed are not very sensitive to errors in the data points. The use of random subsampling of the data points to speed up the computations also is discussed. The techniques developed in this paper can be applied to fitting other kinds of curves as well.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 104-134"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139464058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Computation of pairs of related Gauss-type quadrature rules 计算成对相关的高斯型正交规则

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.03.003

H. Alqahtani , C.F. Borges , D.Lj. Djukić , R.M. Mutavdžić Djukić , L. Reichel , M.M. Spalević

引用次数: 0

A parallel exponential integrator scheme for linear differential equations

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.018

F. Hecht, S.-M. Kaber

引用次数: 0

Discretization methods and their extrapolations for two-dimensional nonlinear Volterra-Urysohn integral equations

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.006

Sohrab Bazm , Pedro Lima , Somayeh Nemati

引用次数: 0

Anderson acceleration. Convergence analysis and applications to equilibrium chemistry 安德森加速收敛分析及在平衡化学中的应用

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.01.022

Rawaa Awada , Jérôme Carrayrou , Carole Rosier

{"title":"Anderson acceleration. Convergence analysis and applications to equilibrium chemistry","authors":"Rawaa Awada , Jérôme Carrayrou , Carole Rosier","doi":"10.1016/j.apnum.2024.01.022","DOIUrl":"10.1016/j.apnum.2024.01.022","url":null,"abstract":"<div><div><span><span>In this paper, we study theoretically and numerically the Anderson acceleration method. First, we extend the convergence results of Anderson's method for a small depth to general nonlinear cases. More precisely, we prove that the Type-I and Type-II Anderson(1) are locally q-linearly convergent if the </span>fixed point<span> map is a contraction with a Lipschitz constant small enough. We then illustrate the effectiveness of the method by applying it to the resolution of chemical equilibria. This test case has been identified as a challenging one because of the high nonlinearity of the chemical system and stiffness of the transport phenomena. The Newton method (usually Newton-Raphson) has been adopted by quite all the equilibrium and reactive transport codes. But the often ill-conditioned </span></span>Jacobian matrix<span><span> and the choice of a bad initial data can lead to </span>convergence problems<span><span>, especially if solute transport produces sharp concentrations profiles. Here we propose to combine the Anderson acceleration method with a particular formulation of the equilibrium system called the method of positive continued fractions (usually used as preconditioning). As shown by the numerical simulations, this approach makes it possible to considerably improve the robustness of the resolution of chemical equilibria algorithms, especially since it is coupled with a strategy to monitor the depth of the Anderson acceleration method in order to control the </span>condition number.</span></span></div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 60-75"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139657122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Parallel cloud solution of large algebraic multivalued systems 大型代数多值系统的并行云解法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.03.012

M.A. Rahhali , T. Garcia , P. Spiteri

引用次数: 0

A GPU-accelerated Lagrangian method for solving the Liouville equation in random differential equation systems

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.09.021

V.J. Bevia, S. Blanes, J.C. Cortés, N. Kopylov, R.J. Villanueva

引用次数: 0

Central composite designs with three missing observations 有三个缺失观测点的中心复合设计

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2023.12.013

K. Alanazi , S.D. Georgiou , C. Koukouvinos , S. Stylianou

{"title":"Central composite designs with three missing observations","authors":"K. Alanazi , S.D. Georgiou , C. Koukouvinos , S. Stylianou","doi":"10.1016/j.apnum.2023.12.013","DOIUrl":"10.1016/j.apnum.2023.12.013","url":null,"abstract":"<div><div>In an experiment, there are many situations when some observations are missed, ignored or unavailable due to some accidents or high cost experiments. A missing observation can make the results of a response surface model quite misleading. This work therefore investigates the impact of a three missing observation of them various design points: factorial, axial and center points, on the estimation and predictive capability of the central composite design (CCD). Therefore minimaxloss CCD is formulated under a minimaxloss criterion. The minimaxloss CCD is considered to be robust to three missing observation and the investigation has been made in this article. The general formulas for the efficiency of the design when missing three observations, are presented in closed form as a function of <em>α</em>, where <em>α</em> is the value used in the CCDs' axial part. For the first time in this paper, these are calculated explicitly for CCDs from <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span> to <span><math><mi>k</mi><mo>=</mo><mn>7</mn></math></span> factors and displayed in tables for practitioners to use. The corresponding graphs for the efficiencies are presented and suggestions are made for the values of <em>α</em> to maximize the robustness and estimability of the design for all cases.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 2-21"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A priori and a posteriori error estimates for efficient numerical schemes for coupled systems of linear and nonlinear singularly perturbed initial-value problems

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.005

Carmelo Clavero , Shashikant Kumar , Sunil Kumar

引用次数: 0

Multilinear algebra methods for higher-dimensional graphs 高维图的多重线性代数方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2023.11.009

Alaeddine Zahir , Khalide Jbilou , Ahmed Ratnani

引用次数: 0