Applied Numerical Mathematics最新文献

A frozen Levenberg-Marquardt-Kaczmarz method with convex penalty terms and two-point gradient strategy for ill-posed problems 带凸惩罚项和两点梯度策略的冷冻莱文伯格-马尔卡特-卡茨马尔兹方法，用于解决难题

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-11-26 DOI: 10.1016/j.apnum.2024.11.014

Xiaoyan Zhang, Guangyu Gao, Zhenwu Fu, Yang Li, Bo Han

{"title":"A frozen Levenberg-Marquardt-Kaczmarz method with convex penalty terms and two-point gradient strategy for ill-posed problems","authors":"Xiaoyan Zhang, Guangyu Gao, Zhenwu Fu, Yang Li, Bo Han","doi":"10.1016/j.apnum.2024.11.014","DOIUrl":"10.1016/j.apnum.2024.11.014","url":null,"abstract":"<div><div>In this paper, we present a frozen iteratively regularized approach for solving ill-posed problems and conduct a thorough analysis of its performance. This method involves incorporating Nesterov's acceleration strategy into the Levenberg-Marquardt-Kaczmarz method and maintaining a constant Fréchet derivative of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> at an initial approximation solution <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> throughout the iterative process, which called the frozen strategy. Moreover, convex functions are employed as penalty terms to capture the distinctive features of solutions. We establish convergence and regularization analysis by leveraging some classical assumptions and properties of convex functions. These theoretical findings are further supported by a number of numerical studies, which demonstrate the efficacy of our approach. Additionally, to verify the impact of initial values on the accuracy of reconstruction, the data-driven strategy is adopted in the third numerical example for comparison.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 187-207"},"PeriodicalIF":2.2,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722723","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

New adaptive low-dissipation central-upwind schemes 新的自适应低耗散中央上风方案

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-11-20 DOI: 10.1016/j.apnum.2024.11.010

Shaoshuai Chu , Alexander Kurganov , Igor Menshov

{"title":"New adaptive low-dissipation central-upwind schemes","authors":"Shaoshuai Chu , Alexander Kurganov , Igor Menshov","doi":"10.1016/j.apnum.2024.11.010","DOIUrl":"10.1016/j.apnum.2024.11.010","url":null,"abstract":"<div><div>We introduce new second-order adaptive low-dissipation central-upwind (LDCU) schemes for the one- and two-dimensional hyperbolic systems of conservation laws. The new adaptive LDCU schemes employ the recently proposed LDCU numerical fluxes computed using the point values reconstructed with the help of adaptively selected nonlinear limiters. To this end, we use a smoothness indicator to detect “rough” parts of the computed solution, where the piecewise linear reconstruction is performed using an overcompressive limiter, which leads to extremely sharp resolution of shock and contact waves. In the “smooth” areas, we use a more dissipative limiter to prevent appearance of artificial kinks and staircase-like structures there. In order to avoid oscillations, we perform the reconstruction in the local characteristic variables obtained using the local characteristic decomposition. We use a smoothness indicator from Löhner (1987) <span><span>[34]</span></span> and apply the developed schemes to the one- and two-dimensional Euler equations of gas dynamics. The obtained numerical results clearly demonstrate that the new adaptive LDCU schemes outperform the original ones.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 155-170"},"PeriodicalIF":2.2,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697462","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

An adaptive DtN-FEM for the scattering problem from orthotropic media 正交各向同性介质散射问题的自适应 DtN-FEM

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-11-20 DOI: 10.1016/j.apnum.2024.11.013

Lei Lin , Junliang Lv , Tian Niu

引用次数: 0

Convergence, divergence, and inherent oscillations in MAS solutions of 2D Laplace-Neumann problems 二维拉普拉斯-诺伊曼问题 MAS 解的收敛、发散和固有振荡

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-11-20 DOI: 10.1016/j.apnum.2024.11.012

Georgios D. Kolezas, George Fikioris, John A. Roumeliotis

引用次数: 0

A priori error estimates for a coseismic slip optimal control problem 同震滑移优化控制问题的先验误差估计

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-11-19 DOI: 10.1016/j.apnum.2024.11.011

Jorge Aguayo , Rodolfo Araya

引用次数: 0

Mixed finite elements of higher-order in elastoplasticity 弹塑性中的高阶混合有限元

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-11-15 DOI: 10.1016/j.apnum.2024.11.008

Patrick Bammer, Lothar Banz, Andreas Schröder

引用次数: 0

A local discontinuous Galerkin methods with local Lax-Friedrichs flux and modified central flux for one dimensional nonlinear convection-diffusion equation 针对一维非线性对流扩散方程的局部非连续伽勒金方法与局部 Lax-Friedrichs 通量和修正的中心通量

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-11-15 DOI: 10.1016/j.apnum.2024.11.009

Jia Li , Wei Guan , Shengzhu Shi , Boying Wu

引用次数: 0

An inertial hybrid DFPM-based algorithm for constrained nonlinear equations with applications 基于惯性混合 DFPM 的约束非线性方程算法及其应用

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-11-15 DOI: 10.1016/j.apnum.2024.11.007

Guodong Ma , Wei Zhang , Jinbao Jian, Zefeng Huang, Jingyi Mo

{"title":"An inertial hybrid DFPM-based algorithm for constrained nonlinear equations with applications","authors":"Guodong Ma , Wei Zhang , Jinbao Jian, Zefeng Huang, Jingyi Mo","doi":"10.1016/j.apnum.2024.11.007","DOIUrl":"10.1016/j.apnum.2024.11.007","url":null,"abstract":"<div><div>The derivative-free projection method (DFPM) is an effective and classic approach for solving the system of nonlinear monotone equations with convex constraints, but the global convergence or convergence rate of the DFPM is typically analyzed under the Lipschitz continuity. This observation motivates us to propose an inertial hybrid DFPM-based algorithm, which incorporates a modified conjugate parameter utilizing a hybridized technique, to weaken the convergence assumption. By integrating an improved inertial extrapolation step and the restart procedure into the search direction, the resulting direction satisfies the sufficient descent and trust region properties, which independent of line search choices. Under weaker conditions, we establish the global convergence and Q-linear convergence rate of the proposed algorithm. To the best of our knowledge, this is the first analysis of the Q-linear convergence rate under the condition that the mapping is locally Lipschitz continuous. Finally, by applying the Bayesian hyperparameter optimization technique, a series of numerical experiment results demonstrate that the new algorithm has advantages in solving nonlinear monotone equation systems with convex constraints and handling compressed sensing problems.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 100-123"},"PeriodicalIF":2.2,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698107","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

A derivative-free projection method with double inertial effects for solving nonlinear equations 用于求解非线性方程的具有双重惯性效应的无导数投影法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-11-14 DOI: 10.1016/j.apnum.2024.11.006

Abdulkarim Hassan Ibrahim , Suliman Al-Homidan

引用次数: 0

Multicomponent signals interference detection exploiting HP-splines frequency parameter 利用 HP 样条频率参数进行多分量信号干扰检测

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-11-14 DOI: 10.1016/j.apnum.2024.11.004

Vittoria Bruni , Rosanna Campagna , Domenico Vitulano

{"title":"Multicomponent signals interference detection exploiting HP-splines frequency parameter","authors":"Vittoria Bruni , Rosanna Campagna , Domenico Vitulano","doi":"10.1016/j.apnum.2024.11.004","DOIUrl":"10.1016/j.apnum.2024.11.004","url":null,"abstract":"<div><div>Multicomponent signals play a key role in many application fields, such as biology, audio processing, seismology, air traffic control and security. They are well represented in the time-frequency plane where they are mainly characterized by special curves, called ridges, which carry information about the instantaneous frequency (IF) of each signal component. However, ridges identification usually is a difficult task for signals having interfering components and requires the automatic localization of time-frequency interference regions (IRs). This paper presents a study on the use of the frequency parameter of a hyperbolic-polynomial penalized spline (HP-spline) to predict the presence of interference regions. Since HP-splines are suitably designed for signal regression, it is proved that their frequency parameter can capture the change caused by the interaction between signal components in the time-frequency representation. In addition, the same parameter allows us to define a data-driven approach for IR localization, namely HP-spline Signal Interference Detection (HP-SID) method. Numerical experiments show that the proposed HP-SID can identify specific interference regions for different types of multicomponent signals by means of an efficient algorithm that does not require explicit data regression.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 20-37"},"PeriodicalIF":2.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697463","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