Pub Date : 2026-01-06DOI: 10.1016/j.rinam.2025.100679
Zixuan Shen , Deyi Ma
In this paper, we establish a Liouville-type theorem for smooth solutions of the stationary Navier–Stokes equations under a growth condition on the Lebesgue norms. Based on this condition, we prove a lemma analogous to the Poincaré-type inequality in the curl sense, which serves as a key tool in proving our main result.
{"title":"A Liouville-type theorem for 3D stationary Navier–Stokes equations","authors":"Zixuan Shen , Deyi Ma","doi":"10.1016/j.rinam.2025.100679","DOIUrl":"10.1016/j.rinam.2025.100679","url":null,"abstract":"<div><div>In this paper, we establish a Liouville-type theorem for smooth solutions of the stationary Navier–Stokes equations under a growth condition on the Lebesgue norms. Based on this condition, we prove a lemma analogous to the Poincaré-type inequality in the curl sense, which serves as a key tool in proving our main result.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100679"},"PeriodicalIF":1.3,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939037","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 : 2026-01-06DOI: 10.1016/j.rinam.2025.100682
S. Mansoori Aref , M.H. Heydari , M. Bayram
In this study, we develop an operational matrix technique to address a set of fractional nonlinear integro-differential equations with the Caputo–Hadamard derivative. We utilize a family of the piecewise Chebyshev cardinal functions as basis functions in this regard. Some formulas are introduced for calculating the classical and Hadamard fractional integrals of these functions. In the established strategy, the fractional expression is approximated utilizing these piecewise functions. By employing the aforementioned operational matrices and leveraging the cardinal property of the basis functions, we solve an algebraic system to obtain the solution. Convergence is both analytically demonstrated and confirmed through numerical experiments. Additionally, we compare the results obtained using this method with those derived from the hat functions method.
{"title":"A numerical framework based on piecewise Chebyshev cardinal functions for fractional integro-differential equations","authors":"S. Mansoori Aref , M.H. Heydari , M. Bayram","doi":"10.1016/j.rinam.2025.100682","DOIUrl":"10.1016/j.rinam.2025.100682","url":null,"abstract":"<div><div>In this study, we develop an operational matrix technique to address a set of fractional nonlinear integro-differential equations with the Caputo–Hadamard derivative. We utilize a family of the piecewise Chebyshev cardinal functions as basis functions in this regard. Some formulas are introduced for calculating the classical and Hadamard fractional integrals of these functions. In the established strategy, the fractional expression is approximated utilizing these piecewise functions. By employing the aforementioned operational matrices and leveraging the cardinal property of the basis functions, we solve an algebraic system to obtain the solution. Convergence is both analytically demonstrated and confirmed through numerical experiments. Additionally, we compare the results obtained using this method with those derived from the hat functions method.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100682"},"PeriodicalIF":1.3,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939035","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 : 2026-01-06DOI: 10.1016/j.rinam.2025.100681
Mohammad Meysami , Ali Lotfi
The screening effect is a central idea in spatial prediction: once nearby observations are used, distant ones add little. While Stein’s classical results explain this effect under strong spectral conditions, many models used in practice fall outside those assumptions. In this paper, we extend Stein’s theory to a broader class of Gaussian random fields. We replace strict regular variation by more flexible O-regular variation, resolve the critical borderline case where the spectral exponent equals the dimension, and derive explicit convergence rates for prediction error. Our analysis also shows that screening is robust to mild nonstationarity and anisotropy, and it applies to irregular sampling designs such as Delone sets. To illustrate these results, we provide examples with Matérn, generalized Cauchy, and anisotropic models, along with numerical experiments confirming the theory. These findings clarify when local kriging can safely replace global prediction, and they provide a solid foundation for scalable methods such as covariance tapering and Vecchia approximations.
{"title":"Screening effects in Gaussian random fields under generalized spectral conditions","authors":"Mohammad Meysami , Ali Lotfi","doi":"10.1016/j.rinam.2025.100681","DOIUrl":"10.1016/j.rinam.2025.100681","url":null,"abstract":"<div><div>The screening effect is a central idea in spatial prediction: once nearby observations are used, distant ones add little. While Stein’s classical results explain this effect under strong spectral conditions, many models used in practice fall outside those assumptions. In this paper, we extend Stein’s theory to a broader class of Gaussian random fields. We replace strict regular variation by more flexible O-regular variation, resolve the critical borderline case where the spectral exponent equals the dimension, and derive explicit convergence rates for prediction error. Our analysis also shows that screening is robust to mild nonstationarity and anisotropy, and it applies to irregular sampling designs such as Delone sets. To illustrate these results, we provide examples with Matérn, generalized Cauchy, and anisotropic models, along with numerical experiments confirming the theory. These findings clarify when local kriging can safely replace global prediction, and they provide a solid foundation for scalable methods such as covariance tapering and Vecchia approximations.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100681"},"PeriodicalIF":1.3,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939036","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 : 2026-01-06DOI: 10.1016/j.rinam.2025.100680
Thomas Batard
This paper deals with the application of a geometric setting widely employed in theoretical physics, namely the fiber bundles, to color image restoration. The key idea of this approach is to model an image as a function on a principal bundle satisfying an equivariance property with respect to the action of a Lie group acting on its pixel values, and which can model the lighting changes in a scene. In this context, a natural tool for the differentiation of an image is by means of a covariant derivative. In previous works, optimal covariant derivatives have been constructed as solutions of a variational model consisting of the minimization of the norm of the covariant derivative of the image, and applied to various tasks in color image restoration through the extension of the Total Variation regularizer to vector bundles. The aim of this paper is to extend these works by constructing optimal second order covariant derivatives as solutions of the minimization of the norm of the second order covariant derivative of the image. Experiments on deblurring and super-resolution corroborate the relevance of the proposed model for color image restoration. More generally, this paper validates the use of the geometric setting of fiber bundles in imaging sciences.
{"title":"Optimal second order covariant derivatives on associated bundles — Application to color image restoration","authors":"Thomas Batard","doi":"10.1016/j.rinam.2025.100680","DOIUrl":"10.1016/j.rinam.2025.100680","url":null,"abstract":"<div><div>This paper deals with the application of a geometric setting widely employed in theoretical physics, namely the fiber bundles, to color image restoration. The key idea of this approach is to model an image as a function on a principal bundle satisfying an equivariance property with respect to the action of a Lie group acting on its pixel values, and which can model the lighting changes in a scene. In this context, a natural tool for the differentiation of an image is by means of a covariant derivative. In previous works, optimal covariant derivatives have been constructed as solutions of a variational model consisting of the minimization of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm of the covariant derivative of the image, and applied to various tasks in color image restoration through the extension of the Total Variation regularizer to vector bundles. The aim of this paper is to extend these works by constructing optimal second order covariant derivatives as solutions of the minimization of the norm of the second order covariant derivative of the image. Experiments on deblurring and super-resolution corroborate the relevance of the proposed model for color image restoration. More generally, this paper validates the use of the geometric setting of fiber bundles in imaging sciences.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100680"},"PeriodicalIF":1.3,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939039","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 : 2026-01-06DOI: 10.1016/j.rinam.2025.100670
Robert Carlson
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial differential equations on domains which are modeled as networks of one dimensional segments joined at nodes.
{"title":"A quantum graph FFT with applications to partial differential equations on networks","authors":"Robert Carlson","doi":"10.1016/j.rinam.2025.100670","DOIUrl":"10.1016/j.rinam.2025.100670","url":null,"abstract":"<div><div>The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial differential equations on domains which are modeled as networks of one dimensional segments joined at nodes.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100670"},"PeriodicalIF":1.3,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939038","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}
This study introduces a hybrid numerical methodology designed to address multi-domain wave propagation problems. The temporal discretization is achieved using the Houbolt scheme, a finite-difference-based approach known for its robust stability in time-dependent simulations. Spatially, the computational domain is partitioned into subdomains via a domain decomposition strategy, with continuity and equilibrium constraints imposed along the interfaces to ensure physical fidelity. Within each subdomain, the meshless generalized finite difference method (GFDM) is employed, thereby avoiding the complexity of mesh generation. Through the integration of Taylor series expansion and moving least squares (MLS) approximation, explicit formulations of partial derivatives are constructed. Numerical experiments confirm that the proposed hybrid method provides high accuracy and stability in simulating multi-domain wave propagation phenomena.
{"title":"A hybrid numerical method for multi-domain wave propagation problems","authors":"Zihui Yan , Xiangran Zheng , Wenzhen Qu , Sheng-Dong Zhao","doi":"10.1016/j.rinam.2025.100678","DOIUrl":"10.1016/j.rinam.2025.100678","url":null,"abstract":"<div><div>This study introduces a hybrid numerical methodology designed to address multi-domain wave propagation problems. The temporal discretization is achieved using the Houbolt scheme, a finite-difference-based approach known for its robust stability in time-dependent simulations. Spatially, the computational domain is partitioned into subdomains via a domain decomposition strategy, with continuity and equilibrium constraints imposed along the interfaces to ensure physical fidelity. Within each subdomain, the meshless generalized finite difference method (GFDM) is employed, thereby avoiding the complexity of mesh generation. Through the integration of Taylor series expansion and moving least squares (MLS) approximation, explicit formulations of partial derivatives are constructed. Numerical experiments confirm that the proposed hybrid method provides high accuracy and stability in simulating multi-domain wave propagation phenomena.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100678"},"PeriodicalIF":1.3,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798445","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 : 2025-12-17DOI: 10.1016/j.rinam.2025.100674
Yalin Tang , Mingjun Li , Shujiang Tang
In this study, we develop a hybrid high-order monotonicity-preserving Weighted Essentially Non-Oscillatory (MPWENO) finite difference discretization for the compressible Euler equations. The key innovation of this scheme lies in optimizing the numerical flux through the mixed smooth indicator to reduce the numerical oscillations caused by scheme conversion, and adjusting the reference value to modify the MP limiter, thereby enabling the scheme to achieve the required numerical accuracy while maintaining monotonicity. The novelty of this work lies in systematically adjusting the numerical fluxes by using the mixed smooth indicator to distinguish between discontinuities and extrema and improving the accuracy of the reference value to change the MP limiter, which is different from other MP schemes. The proposed method improves the accuracy at the extreme points, exhibits outstanding robustness and excellent resolution, making it particularly suitable for solving complex problems in compressible Euler equations. Moreover, it is easy to implement and applicable to multi-dimensional problems, with significant practical advantages. Numerical results show that this method has high accuracy, strong robustness, and high resolution. These findings highlight the effectiveness and reliability of this method in handling complex compressible flow simulations.
{"title":"A hybrid MPWENO scheme with enhanced accuracy and robustness for the compressible Euler equations","authors":"Yalin Tang , Mingjun Li , Shujiang Tang","doi":"10.1016/j.rinam.2025.100674","DOIUrl":"10.1016/j.rinam.2025.100674","url":null,"abstract":"<div><div>In this study, we develop a hybrid high-order monotonicity-preserving Weighted Essentially Non-Oscillatory (MPWENO) finite difference discretization for the compressible Euler equations. The key innovation of this scheme lies in optimizing the numerical flux through the mixed smooth indicator to reduce the numerical oscillations caused by scheme conversion, and adjusting the reference value to modify the MP limiter, thereby enabling the scheme to achieve the required numerical accuracy while maintaining monotonicity. The novelty of this work lies in systematically adjusting the numerical fluxes by using the mixed smooth indicator to distinguish between discontinuities and extrema and improving the accuracy of the reference value to change the MP limiter, which is different from other MP schemes. The proposed method improves the accuracy at the extreme points, exhibits outstanding robustness and excellent resolution, making it particularly suitable for solving complex problems in compressible Euler equations. Moreover, it is easy to implement and applicable to multi-dimensional problems, with significant practical advantages. Numerical results show that this method has high accuracy, strong robustness, and high resolution. These findings highlight the effectiveness and reliability of this method in handling complex compressible flow simulations.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100674"},"PeriodicalIF":1.3,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798442","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 : 2025-12-06DOI: 10.1016/j.rinam.2025.100677
Jiadong Qiu , Xiang Liu , Feng Liao
In this paper, general conservative sixth- and eighth-order compact finite difference schemes are presented to solve the N-coupled nonlinear Schrödinger-Boussinesq equations numerically. The existence of the difference solution is proved by fixed-point theorem. By utilizing the discrete energy methods, the proposed difference schemes are proved to be unconditionally convergent at the order with mesh-size and time step in the discrete -norm. By using the Yoshida’s composition method, we improve the scheme (3.1)-(3.3) with a group of given time-step increments repeatedly and then obtain a temporal fourth-order difference scheme. Numerical experiments confirm the theoretical results and verify the accuracy and efficiency of our method.
{"title":"General conservative sixth- and eighth-order compact finite difference schemes for the N-coupled Schrödinger-Boussinesq equations","authors":"Jiadong Qiu , Xiang Liu , Feng Liao","doi":"10.1016/j.rinam.2025.100677","DOIUrl":"10.1016/j.rinam.2025.100677","url":null,"abstract":"<div><div>In this paper, general conservative sixth- and eighth-order compact finite difference schemes are presented to solve the N-coupled nonlinear Schrödinger-Boussinesq equations numerically. The existence of the difference solution is proved by fixed-point theorem. By utilizing the discrete energy methods, the proposed difference schemes are proved to be unconditionally convergent at the order <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>8</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> with mesh-size <span><math><mi>h</mi></math></span> and time step <span><math><mi>τ</mi></math></span> in the discrete <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span>-norm. By using the Yoshida’s composition method, we improve the scheme <span><span>(3.1)</span></span>-<span><span>(3.3)</span></span> with a group of given time-step increments repeatedly and then obtain a temporal fourth-order difference scheme. Numerical experiments confirm the theoretical results and verify the accuracy and efficiency of our method.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100677"},"PeriodicalIF":1.3,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693047","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 : 2025-11-01DOI: 10.1016/j.rinam.2025.100667
Peipei Zhao , Pengyu Zhang
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.
{"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}
Pub Date : 2025-11-01DOI: 10.1016/j.rinam.2025.100666
Qiang Niu , Mianmian Chen , Jinheng Wu
The Lanczos algorithm is a well-known three-term recurrence that can be used to generate an orthogonal basis for a Krylov subspace derived by a symmetric matrix. In the paper, we present a statistical interpretation of the entries of the tridiagonal matrix generated by the Lanczos process with a diagonal matrix and an initial vector . We show that the entries on the main diagonal line can be interpreted as weighted mean and the entries on the super-diagonal line can be understood as weighted sum of variance. Besides, a recurrence for producing the entries on the off-diagonal entries of the tridiagonal matrix is discovered, which leads to a new implementation of the Lanczos process. Finally, numerical examples are provided to investigate the preservation of orthogonality and efficiency in data fitting.
{"title":"Lanczos algorithm explained in statistics","authors":"Qiang Niu , Mianmian Chen , Jinheng Wu","doi":"10.1016/j.rinam.2025.100666","DOIUrl":"10.1016/j.rinam.2025.100666","url":null,"abstract":"<div><div>The Lanczos algorithm is a well-known three-term recurrence that can be used to generate an orthogonal basis for a Krylov subspace derived by a symmetric matrix. In the paper, we present a statistical interpretation of the entries of the tridiagonal matrix generated by the Lanczos process with a diagonal matrix <span><math><mi>X</mi></math></span> and an initial vector <span><math><mi>e</mi></math></span>. We show that the entries on the main diagonal line can be interpreted as <em>weighted mean</em> and the entries on the super-diagonal line can be understood as <em>weighted sum of variance</em>. Besides, a recurrence for producing the entries on the off-diagonal entries of the tridiagonal matrix is discovered, which leads to a new implementation of the Lanczos process. Finally, numerical examples are provided to investigate the preservation of orthogonality and efficiency in data fitting.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100666"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145519627","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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