In this paper, we study the Galerkin method for obtaining approximate solutions to linear Fredholm integral equations of the second kind. The finite element solution is represented as a linear combination of basis functions, and the construction of suitable basis functions plays a crucial role in the accuracy of the approximation. We propose an optimal interpolation formula that exactly reproduces the functions and , and derive basis functions from its coefficients. This interpolation formula is constructed within the Hilbert space . To evaluate the effectiveness of the proposed approach, we solve several integral equations using the Galerkin method with two types of basis functions: the newly constructed exponential basis and classical piecewise linear basis functions. Numerical experiments are presented to compare the accuracy of these approaches. Graphs and tables illustrate the approximation errors, demonstrating that both basis functions achieve an error order of , with the optimal interpolation-based basis yielding superior accuracy in certain cases.
{"title":"The numerical solution of a Fredholm integral equation of the second kind using the Galerkin method based on optimal interpolation","authors":"Samandar Babaev , Abdullo Hayotov , Asliddin Boltaev , Surayyo Mirzoyeva , Malika Mirzaeva","doi":"10.1016/j.rinam.2025.100607","DOIUrl":"10.1016/j.rinam.2025.100607","url":null,"abstract":"<div><div>In this paper, we study the Galerkin method for obtaining approximate solutions to linear Fredholm integral equations of the second kind. The finite element solution is represented as a linear combination of basis functions, and the construction of suitable basis functions plays a crucial role in the accuracy of the approximation. We propose an optimal interpolation formula that exactly reproduces the functions <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>x</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>x</mi></mrow></msup></math></span>, and derive basis functions from its coefficients. This interpolation formula is constructed within the Hilbert space <span><math><msubsup><mrow><mi>W</mi></mrow><mrow><mn>2</mn></mrow><mrow><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mrow></msubsup></math></span>. To evaluate the effectiveness of the proposed approach, we solve several integral equations using the Galerkin method with two types of basis functions: the newly constructed exponential basis and classical piecewise linear basis functions. Numerical experiments are presented to compare the accuracy of these approaches. Graphs and tables illustrate the approximation errors, demonstrating that both basis functions achieve an error order of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>h</mi><mo>)</mo></mrow></mrow></math></span>, with the optimal interpolation-based basis yielding superior accuracy in certain cases.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100607"},"PeriodicalIF":1.4,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338603","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}
Pub Date : 2025-06-20DOI: 10.1016/j.rinam.2025.100605
Guoqiang Zhao, Dongxi Li
Cancer subtype analysis faces challenges due to limited availability of gene samples and the complexity of cancer gene expression data. The imbalance of Positive and negative category ratio and high-dimensional redundant information degrade prediction performance. This paper proposes an integrated extreme random forest with feature selection model TreeEM(Tree-enhanced Ensemble Model combining with feature selection) to enhance prediction ability and reduce computational costs. The TreeEM model combines the Max-Relevance and Min-Redundancy(MRMR) feature selection method with improved fusion undersampling random forest and extreme tree forest. The TreeEM model achieves excellent performance on three cancer datasets, especially on the multi-omics datasets BRCA(Breast Cancer) and ARCENE datasets, with average improvements of 7.90% and 1.90% in prediction accuracy, respectively. This model also uses TCGA data with known survival time for survival analysis and prediction, demonstrating the reliability of the TreeEM model. This work contributes to advancements in computational tools for cancer research, facilitating precision medicine approaches and improving decision-making. The above results provide new ideas for cancer subtype classification, but the existing methods still have limitations in data imbalance and high-dimensional feature processing. In the following section, the shortcomings of the current research and the innovative solutions of this paper are systematically described.
由于基因样本的有限可用性和癌症基因表达数据的复杂性，癌症亚型分析面临挑战。正负类比失衡和高维冗余信息会降低预测性能。为了提高预测能力和降低计算成本，本文提出了一种带有特征选择模型TreeEM（Tree-enhanced Ensemble model and feature selection）的集成极端随机森林模型。该模型将最大相关和最小冗余（MRMR）特征选择方法与改进的融合欠采样随机森林和极端树森林相结合。TreeEM模型在三个癌症数据集上取得了优异的表现，特别是在多组学数据集BRCA（Breast cancer）和ARCENE数据集上，预测准确率平均分别提高了7.90%和1.90%。该模型还使用已知生存时间的TCGA数据进行生存分析和预测，证明了TreeEM模型的可靠性。这项工作有助于癌症研究的计算工具的进步，促进精准医学方法和改进决策。上述结果为癌症亚型分类提供了新的思路，但现有方法在数据不平衡、高维特征处理等方面仍存在局限性。在接下来的部分中，系统地描述了当前研究的不足和本文的创新解决方案。
{"title":"TreeEM: Tree-enhanced ensemble model combining with feature selection for cancer subtype classification and survival prediction","authors":"Guoqiang Zhao, Dongxi Li","doi":"10.1016/j.rinam.2025.100605","DOIUrl":"10.1016/j.rinam.2025.100605","url":null,"abstract":"<div><div>Cancer subtype analysis faces challenges due to limited availability of gene samples and the complexity of cancer gene expression data. The imbalance of Positive and negative category ratio and high-dimensional redundant information degrade prediction performance. This paper proposes an integrated extreme random forest with feature selection model TreeEM(Tree-enhanced Ensemble Model combining with feature selection) to enhance prediction ability and reduce computational costs. The TreeEM model combines the Max-Relevance and Min-Redundancy(MRMR) feature selection method with improved fusion undersampling random forest and extreme tree forest. The TreeEM model achieves excellent performance on three cancer datasets, especially on the multi-omics datasets BRCA(Breast Cancer) and ARCENE datasets, with average improvements of 7.90% and 1.90% in prediction accuracy, respectively. This model also uses TCGA data with known survival time for survival analysis and prediction, demonstrating the reliability of the TreeEM model. This work contributes to advancements in computational tools for cancer research, facilitating precision medicine approaches and improving decision-making. The above results provide new ideas for cancer subtype classification, but the existing methods still have limitations in data imbalance and high-dimensional feature processing. In the following section, the shortcomings of the current research and the innovative solutions of this paper are systematically described.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100605"},"PeriodicalIF":1.4,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321581","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}
Pub Date : 2025-06-18DOI: 10.1016/j.rinam.2025.100602
Pengfei Luo , Yun Zhang , Lu Xu
The directional motivation of predator is influenced by the density of prey and its alarm call, this paper focuses on a three-species spatial intraguild predation model involving prey-taxis and alarm-taxis. By energy estimates and heat semigroup theory, we prove that this model possesses a bounded and global classical solution in -dimensional space () with Neumann boundary conditions.
{"title":"Global boundedness of a three-species spatial intraguild predation model with alarm-taxis","authors":"Pengfei Luo , Yun Zhang , Lu Xu","doi":"10.1016/j.rinam.2025.100602","DOIUrl":"10.1016/j.rinam.2025.100602","url":null,"abstract":"<div><div>The directional motivation of predator is influenced by the density of prey and its alarm call, this paper focuses on a three-species spatial intraguild predation model involving prey-taxis and alarm-taxis. By energy estimates and heat semigroup theory, we prove that this model possesses a bounded and global classical solution in <span><math><mi>N</mi></math></span>-dimensional space (<span><math><mrow><mi>N</mi><mo>≥</mo><mn>3</mn></mrow></math></span>) with Neumann boundary conditions.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100602"},"PeriodicalIF":1.4,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307320","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}
Pub Date : 2025-06-16DOI: 10.1016/j.rinam.2025.100599
Jean-Baptiste Leroux, Matthieu Sacher
Five non-tabulated integrals are analytically calculated. These integrals emerge from the linear theory of partially cavitating hydrofoils and propeller blades. They appear in a series of weight functions involved in the determination of the cavitation number and cavity shape. The present analytical results eliminate the need for unnecessary numerical integrations, which could be beneficial in reducing computational costs and improving the robustness of numerical models.
{"title":"Analytical computation of five unresolved integrals in the linear theory of partially cavitating hydrofoils","authors":"Jean-Baptiste Leroux, Matthieu Sacher","doi":"10.1016/j.rinam.2025.100599","DOIUrl":"10.1016/j.rinam.2025.100599","url":null,"abstract":"<div><div>Five non-tabulated integrals are analytically calculated. These integrals emerge from the linear theory of partially cavitating hydrofoils and propeller blades. They appear in a series of weight functions involved in the determination of the cavitation number and cavity shape. The present analytical results eliminate the need for unnecessary numerical integrations, which could be beneficial in reducing computational costs and improving the robustness of numerical models.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100599"},"PeriodicalIF":1.4,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144298102","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}
Pub Date : 2025-06-16DOI: 10.1016/j.rinam.2025.100604
Cheng Chen , Wenting Shao
For solving the KdV equation, a novel numerical method with high order accuracy in both space and time is proposed. In the spatial direction, Sinc collocation method, which has the property of exponential convergence, is adopted. In the temporal direction, the variable stepsize Runge–Kutta-embedded pair RKq(p) is utilized. Sinc collocation method is applicable when the approximated function satisfies the exponential decay as the spatial variable tends to infinity, this characteristic is consistent with the one of the soliton solution of the KdV equation. For practical computation, a sufficiently large finite domain is taken, on which the differential matrices with respect to the discrete points are constructed. A new adaptive strategy is proposed to enhance the robustness of the variable stepsize algorithm. In the numerical experiment, four embedded pairs including RK5(4), RK6(5), RK8(7) and RK9(8) are investigated in terms of accuracy, CPU time, the minimum, average and maximum time stepsizes. The numerical results show that RK8(7) has a better performance in the computational efficiency, it achieves higher accuracy with significantly less CPU time. Besides, the KdV-Burgers equation with nonhomogeneous Dirichlet boundary condition imposed on a general interval is considered. The single-exponential transformation and double-exponential transformation are involved. We show that Sinc collocation method, enhanced by exponential transformations, provides an effective numerical approximation for this problem.
{"title":"A kind of adaptive variable stepsize embedded Runge–Kutta pairs coupled with the Sinc collocation method for solving the KdV equation","authors":"Cheng Chen , Wenting Shao","doi":"10.1016/j.rinam.2025.100604","DOIUrl":"10.1016/j.rinam.2025.100604","url":null,"abstract":"<div><div>For solving the KdV equation, a novel numerical method with high order accuracy in both space and time is proposed. In the spatial direction, Sinc collocation method, which has the property of exponential convergence, is adopted. In the temporal direction, the variable stepsize Runge–Kutta-embedded pair RKq(p) is utilized. Sinc collocation method is applicable when the approximated function satisfies the exponential decay as the spatial variable tends to infinity, this characteristic is consistent with the one of the soliton solution of the KdV equation. For practical computation, a sufficiently large finite domain is taken, on which the differential matrices with respect to the discrete points are constructed. A new adaptive strategy is proposed to enhance the robustness of the variable stepsize algorithm. In the numerical experiment, four embedded pairs including RK5(4), RK6(5), RK8(7) and RK9(8) are investigated in terms of accuracy, CPU time, the minimum, average and maximum time stepsizes. The numerical results show that RK8(7) has a better performance in the computational efficiency, it achieves higher accuracy with significantly less CPU time. Besides, the KdV-Burgers equation with nonhomogeneous Dirichlet boundary condition imposed on a general interval is considered. The single-exponential transformation and double-exponential transformation are involved. We show that Sinc collocation method, enhanced by exponential transformations, provides an effective numerical approximation for this problem.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100604"},"PeriodicalIF":1.4,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144291511","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}
Pub Date : 2025-06-13DOI: 10.1016/j.rinam.2025.100601
P. Senfiazad , M.H. Heydari , M. Bayram , D. Baleanu
This paper introduces a new class of tempered fractional quadratic integro-differential equations using the Caputo fractional derivative. The existence and uniqueness of solutions to these equations are analyzed. A numerical method based on the shifted Jacobi polynomials is developed to solve these equations. To execute the proposed method, two operational matrices corresponding to the ordinary and Riemann–Liouville tempered fractional integrals of these polynomials are extracted. In the developed method, the tempered fractional derivative term is initially represented as a linear combination of the aforementioned polynomials with some unknown coefficients. Then, by applying the Riemann–Liouville tempered fractional integral to the expressed polynomials and utilizing their fractional integral operational matrix, an approximation of the unknown solution is defined based on these polynomials and the introduced coefficients. Subsequently, by substituting these approximations into the problem under consideration, and applying the operational matrix of ordinary integral to the shifted Jacobi polynomials, along with utilizing their orthogonality, an approximate solution to the original problem is obtained by solving a nonlinear system of algebraic equations. The convergence of the proposed method is analyzed theoretically and demonstrated through numerical examples. Furthermore, the stability of the solutions is analyzed.
{"title":"A numerical method based on the shifted Jacobi polynomials for a class of tempered fractional quadratic integro-differential equations","authors":"P. Senfiazad , M.H. Heydari , M. Bayram , D. Baleanu","doi":"10.1016/j.rinam.2025.100601","DOIUrl":"10.1016/j.rinam.2025.100601","url":null,"abstract":"<div><div>This paper introduces a new class of tempered fractional quadratic integro-differential equations using the Caputo fractional derivative. The existence and uniqueness of solutions to these equations are analyzed. A numerical method based on the shifted Jacobi polynomials is developed to solve these equations. To execute the proposed method, two operational matrices corresponding to the ordinary and Riemann–Liouville tempered fractional integrals of these polynomials are extracted. In the developed method, the tempered fractional derivative term is initially represented as a linear combination of the aforementioned polynomials with some unknown coefficients. Then, by applying the Riemann–Liouville tempered fractional integral to the expressed polynomials and utilizing their fractional integral operational matrix, an approximation of the unknown solution is defined based on these polynomials and the introduced coefficients. Subsequently, by substituting these approximations into the problem under consideration, and applying the operational matrix of ordinary integral to the shifted Jacobi polynomials, along with utilizing their orthogonality, an approximate solution to the original problem is obtained by solving a nonlinear system of algebraic equations. The convergence of the proposed method is analyzed theoretically and demonstrated through numerical examples. Furthermore, the stability of the solutions is analyzed.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100601"},"PeriodicalIF":1.4,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270417","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}
Pub Date : 2025-05-01DOI: 10.1016/j.rinam.2025.100561
Miao-miao Song , Zui-cha Deng , Xiang Li , Qiu Cui
In this paper, we study the convergence of the inverse drift rate problem of option pricing based on degenerate parabolic equations, aiming to recover the stock price drift rate function by known option market prices. Unlike the classical inverse parabolic equation problem, the article transforms the original problem into an inverse problem with principal coefficients of the degenerate parabolic equation over a bounded region by variable substitution, thus avoiding the error introduced by artificial truncation. Under the optimal control framework, the problem is transformed into an optimization problem, the existence of the minimal solution is proved, and a mathematical proof of the convergence of the optimal solution is given. Finally, the gradient-type iterative method is applied to obtain the numerical solution of the inverse problem, and numerical experiments are conducted to verify it. This study provides an effective theoretical framework and numerical method for inferring the stock price drift rate from the option market price.
{"title":"Convergence analysis of option drift rate inverse problem based on degenerate parabolic equation","authors":"Miao-miao Song , Zui-cha Deng , Xiang Li , Qiu Cui","doi":"10.1016/j.rinam.2025.100561","DOIUrl":"10.1016/j.rinam.2025.100561","url":null,"abstract":"<div><div>In this paper, we study the convergence of the inverse drift rate problem of option pricing based on degenerate parabolic equations, aiming to recover the stock price drift rate function by known option market prices. Unlike the classical inverse parabolic equation problem, the article transforms the original problem into an inverse problem with principal coefficients of the degenerate parabolic equation over a bounded region by variable substitution, thus avoiding the error introduced by artificial truncation. Under the optimal control framework, the problem is transformed into an optimization problem, the existence of the minimal solution is proved, and a mathematical proof of the convergence of the optimal solution is given. Finally, the gradient-type iterative method is applied to obtain the numerical solution of the inverse problem, and numerical experiments are conducted to verify it. This study provides an effective theoretical framework and numerical method for inferring the stock price drift rate from the option market price.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100561"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895722","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}
Pub Date : 2025-05-01DOI: 10.1016/j.rinam.2025.100590
Abdelhafid Younsi
This paper is interested in the existence of singularities for solutions of the Navier–Stokes equations in the whole space. We demonstrate the existence of initial data that leads to the unboundedness of the corresponding strong solution within a finite time. Our approach relies on lower and upper bounds of rates of decay for solutions to the Navier–Stokes equations. This result provides valuable insights into significant open problems in both physics and mathematics.
{"title":"A condition for the finite time blow up of the incompressible Navier–Stokes equations in the whole space","authors":"Abdelhafid Younsi","doi":"10.1016/j.rinam.2025.100590","DOIUrl":"10.1016/j.rinam.2025.100590","url":null,"abstract":"<div><div>This paper is interested in the existence of singularities for solutions of the Navier–Stokes equations in the whole space. We demonstrate the existence of initial data that leads to the unboundedness of the corresponding strong solution within a finite time. Our approach relies on lower and upper bounds of rates of decay for solutions to the Navier–Stokes equations. This result provides valuable insights into significant open problems in both physics and mathematics.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100590"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144167461","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}
Pub Date : 2025-05-01DOI: 10.1016/j.rinam.2025.100597
Soumia EL OMARI, Said Melliani
This study investigates the existence of weak solutions for nonlinear anisotropic elliptic equations characterized by non-local boundary conditions within anisotropic weighted variable exponent Sobolev spaces. By employing variational methods and compact embedding theorems tailored to anisotropic Sobolev spaces, the research focuses on understanding the impact of anisotropy, non-locality, and weighted structures on the solution behavior. We establish sufficient conditions for the existence of solutions under various boundary conditions. These results deepen the understanding of anisotropic elliptic problems by highlighting the role of weighted structures and variable exponents in the interaction between anisotropy and non-locality. The study also explores non-local boundary conditions, which may include integrals of the unknown function over parts of the domain or non-local operators, often encountered in applications such as well modeling in 3D stratified petroleum reservoirs with arbitrary geometries. This work provides a solid theoretical foundation for broader applications in engineering and physics.
{"title":"Study of nonlinear anisotropic elliptic problems with non-local boundary conditions in weighted variable exponent Sobolev spaces","authors":"Soumia EL OMARI, Said Melliani","doi":"10.1016/j.rinam.2025.100597","DOIUrl":"10.1016/j.rinam.2025.100597","url":null,"abstract":"<div><div>This study investigates the existence of weak solutions for nonlinear anisotropic elliptic equations characterized by non-local boundary conditions within anisotropic weighted variable exponent Sobolev spaces. By employing variational methods and compact embedding theorems tailored to anisotropic Sobolev spaces, the research focuses on understanding the impact of anisotropy, non-locality, and weighted structures on the solution behavior. We establish sufficient conditions for the existence of solutions under various boundary conditions. These results deepen the understanding of anisotropic elliptic problems by highlighting the role of weighted structures and variable exponents in the interaction between anisotropy and non-locality. The study also explores non-local boundary conditions, which may include integrals of the unknown function over parts of the domain or non-local operators, often encountered in applications such as well modeling in 3D stratified petroleum reservoirs with arbitrary geometries. This work provides a solid theoretical foundation for broader applications in engineering and physics.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100597"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241790","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}
Pub Date : 2025-05-01DOI: 10.1016/j.rinam.2025.100578
Wan-Yi Chiu
The standard mean–variance analysis employs quadratic optimization to determine the optimal portfolio weights and to plot the mean–variance efficient frontier (MVEF). It then indirectly evaluates the mean–variance efficiency test (MVET) by considering the maximum Sharpe ratios of the tangency portfolio within the MVEF framework, which assumes a risk-free rate. This paper integrates these procedures without considering the risk-free rate by transitioning to a regression-based efficient frontier (RBEF). The RBEF estimates the optimal portfolio weights and simultaneously implements the MVET based on an OLS F-test, offering a simpler approach to portfolio optimization.
{"title":"The regression-based efficient frontier","authors":"Wan-Yi Chiu","doi":"10.1016/j.rinam.2025.100578","DOIUrl":"10.1016/j.rinam.2025.100578","url":null,"abstract":"<div><div>The standard mean–variance analysis employs quadratic optimization to determine the optimal portfolio weights and to plot the mean–variance efficient frontier (MVEF). It then indirectly evaluates the mean–variance efficiency test (MVET) by considering the maximum Sharpe ratios of the tangency portfolio within the MVEF framework, which assumes a risk-free rate. This paper integrates these procedures without considering the risk-free rate by transitioning to a regression-based efficient frontier (RBEF). The RBEF estimates the optimal portfolio weights and simultaneously implements the MVET based on an OLS F-test, offering a simpler approach to portfolio optimization.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100578"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899327","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}
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