Results in Applied Mathematics最新文献_第7页

Multicriteria adjustable robustness 多准则可调稳健性

IF 1.3

Results in Applied Mathematics Pub Date : 2025-11-01 Epub Date: 2025-11-27 DOI: 10.1016/j.rinam.2025.100675

Elisabeth Halser, Elisabeth Finhold, Neele Leithäuser, Jan Schwientek, Katrin Teichert, Karl-Heinz Küfer

{"title":"Multicriteria adjustable robustness","authors":"Elisabeth Halser, Elisabeth Finhold, Neele Leithäuser, Jan Schwientek, Katrin Teichert, Karl-Heinz Küfer","doi":"10.1016/j.rinam.2025.100675","DOIUrl":"10.1016/j.rinam.2025.100675","url":null,"abstract":"<div><div>Multicriteria adjustable robust optimization (MARO) problems are highly relevant for a wide variety of practical problems with a two-stage-decision, typically an initial purchase decision followed by the possibility to react during operation after uncertain parameters are revealed. However, no general approaches for the definition of efficient solutions to this problem class are available in the literature for the multicriteria case. The objective of this paper is to find a meaningful definition that in particular allows the computation of solutions. By combining well-known approaches from multicriteria optimization and robust optimization in a straightforward way, we give different definitions for efficient solutions to MARO problems and look at three computation-oriented approaches to deal with the problems. These computation-oriented approaches can also be understood as additional efficiency definitions. We assess the advantages and disadvantages of the different computation-oriented approaches and analyze their connections to our initial definitions of MARO-efficiency. We observe that an <span><math><mi>ɛ</mi></math></span>-constraint inspired first-scalarize-then-robustify approach is beneficial because it provides an efficient set that is easy to understand for decision makers and provides tight bounds on the worst-case evaluation for a particular efficient solution. In contrast, a weighted sum first-scalarize-then-robustify approach keeps the problem structure more simple but the efficient set might look ambiguous. Further, we demonstrate that a first-robustify procedure only gives bad bounds and can be too optimistic as well as too pessimistic.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100675"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145614873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Computing the zeros of cross-product combinations of the Bessel functions with complex order 计算复阶贝塞尔函数的叉积组合的零点

IF 1.3

Results in Applied Mathematics Pub Date : 2025-11-01 Epub Date: 2025-10-06 DOI: 10.1016/j.rinam.2025.100642

Jeff Kershaw, Takayuki Obata

{"title":"Computing the zeros of cross-product combinations of the Bessel functions with complex order","authors":"Jeff Kershaw, Takayuki Obata","doi":"10.1016/j.rinam.2025.100642","DOIUrl":"10.1016/j.rinam.2025.100642","url":null,"abstract":"<div><div>The zeros of cross-product combinations of the Bessel functions are often required as the eigenvalues in boundary-value problems with annular or tubular symmetry. Numerical methods to calculate the roots when the order is real have existed for many years, but those methods are unreliable when the order is complex, probably because the distribution of the zeros in the complex plane is unknown. In this work asymptotic expansions for the Bessel cross-product functions are constructed and used to investigate the root distribution in the complex plane for complex order. When the argument of the order is positive (or negative) the zeros are symmetrically positioned in the first & third (or second & fourth) quadrants of the complex plane. Within a particular quadrant, it is shown that the roots lie on or near to three lines that intersect at a single point. Two of these lines have a finite number of zeros associated with them, while the third line always has an infinite number of roots distributed along it. Approximations to the roots are constructed and used as initial values in an algorithm that more closely estimates the zeros. A longstanding issue with regard to the “exceptional” nature of the lowest root of one of the Bessel cross-product functions when the order is real has also been resolved.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100642"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Lanczos algorithm explained in statistics 统计学解释Lanczos算法

IF 1.3

Results in Applied Mathematics Pub Date : 2025-11-01 Epub Date: 2025-11-10 DOI: 10.1016/j.rinam.2025.100666

Qiang Niu , Mianmian Chen , Jinheng Wu

引用次数: 0

A parameterized Schur complement preconditioner for linear system arising from additive HQ image restoration 加性HQ图像恢复线性系统的参数化Schur补预条件

IF 1.3

Results in Applied Mathematics Pub Date : 2025-11-01 Epub Date: 2025-11-15 DOI: 10.1016/j.rinam.2025.100667

Peipei Zhao , Pengyu Zhang

{"title":"A parameterized Schur complement preconditioner for linear system arising from additive HQ image restoration","authors":"Peipei Zhao , Pengyu Zhang","doi":"10.1016/j.rinam.2025.100667","DOIUrl":"10.1016/j.rinam.2025.100667","url":null,"abstract":"<div><div>Image restoration is to estimate the clean image from the recorded image, it is a highly ill-posed inverse problem. Regularization method is an important approach for solving such problem, which can usually be achieved by minimizing a cost function consisting of a data-fidelity term and a regularization term. In this paper, we consider the additive half-quadratic (HQ) regularized method for image restoration problem, and utilize the Newton method to solve the resulting minimization problem. At each Newton iteration step, a system of linear equations with symmetric positive definite coefficient matrix arises. In order to solve the linear system efficiently, we design a parameterized approximation matrix of the Schur complement inverse matrix, and construct a block preconditioner with parameter correspondingly, according to the block triangular factorization of coefficient matrix and the form of its Schur complement, then the preconditioned conjugate gradient (PCG) method is applied to solve the linear system of equations. Spectral analyses of the preconditioned matrix are also given, numerical experimental results demonstrate the effectiveness of the proposed parameterized preconditioner for solving linear system arising from additive HQ image restoration problem.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100667"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145519626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Second-order finite element scheme of the viscous Cahn–Hilliard equation with energy-stable method 粘性Cahn-Hilliard方程的二阶能量稳定有限元格式

IF 1.3

Results in Applied Mathematics Pub Date : 2025-11-01 Epub Date: 2025-10-22 DOI: 10.1016/j.rinam.2025.100656

WenYan Tian , Hongen Jia

引用次数: 0

The effect of inventory on asset prices 存货对资产价格的影响

IF 1.3

Results in Applied Mathematics Pub Date : 2025-11-01 Epub Date: 2025-10-01 DOI: 10.1016/j.rinam.2025.100650

Jiaqi Hou , Jing Wang , Zhi Yang

引用次数: 0

Optimal error estimates of BDF2 finite element method for the two-dimensional time-dependent Schrödinger equation 二维时间相关Schrödinger方程的BDF2有限元法最优误差估计

IF 1.3

Results in Applied Mathematics Pub Date : 2025-11-01 Epub Date: 2025-11-04 DOI: 10.1016/j.rinam.2025.100663

Zhikun Tian , Jianyun Wang , Zixin Zhong

引用次数: 0

Analytical and numerical investigation of wave resonance over rectangular basin with submerged triangular breakwaters 三角形防波堤淹没下矩形盆地波浪共振的解析与数值研究

IF 1.3

Results in Applied Mathematics Pub Date : 2025-11-01 Epub Date: 2025-10-31 DOI: 10.1016/j.rinam.2025.100655

Ikha Magdalena , Anwar Efendi Nasution

引用次数: 0

Second-order finite element discretization of Stokes equations on convex polygonal meshes 凸多边形网格上Stokes方程的二阶有限元离散化

IF 1.3

Results in Applied Mathematics Pub Date : 2025-11-01 Epub Date: 2025-11-26 DOI: 10.1016/j.rinam.2025.100672

Yanyan Song , Yanqiu Wang , Qiao Xin

引用次数: 0

Sparse PCA via matrix (2,1)-norm regularization with an application to feature selection 基于矩阵（2,1）范数正则化的稀疏PCA及其在特征选择中的应用

IF 1.3

Results in Applied Mathematics Pub Date : 2025-11-01 Epub Date: 2025-12-01 DOI: 10.1016/j.rinam.2025.100676

Li Wang , Jiawei Wang , Ren-Cang Li

{"title":"Sparse PCA via matrix (2,1)-norm regularization with an application to feature selection","authors":"Li Wang , Jiawei Wang , Ren-Cang Li","doi":"10.1016/j.rinam.2025.100676","DOIUrl":"10.1016/j.rinam.2025.100676","url":null,"abstract":"<div><div>This paper is concerned with sparse PCA via the matrix (2,1)-norm regularization (<span><math><msub><mrow><mo>PCA</mo></mrow><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></math></span>). It can produce a row-sparse projection, a useful tool in machine learning when it comes to, for example, feature selection, that aims to choose most relevant features. Mathematically, <span><math><msub><mrow><mo>PCA</mo></mrow><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></math></span> is a non-smooth optimization problem on the Stiefel manifold. For a suitably chosen regularization parameter, the optimal projection matrix has many negligible rows. A practical NEPv approach (nonlinear eigenvalue problem with eigenvector dependency) is proposed to iteratively compute the optimal projection matrix. It is shown that the approach is globally convergent in the sense that the objective is monotonically increasing during the iterative process and any accumulation point of the iterates is a stationary point to the optimization problem. Extensive numerical experiments, with an application to feature selection, have been conducted to demonstrate the performance of the practical NEPv approach, with comparison against existing feature selection methods in terms of classification accuracy. The numerical results demonstrate that <span><math><msub><mrow><mo>PCA</mo></mrow><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></math></span> is highly effective and often produces superior classification results to existing feature selection methods that are in use today.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100676"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145680919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0