IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v325y2018icp120-145.html

Regularized moving least-square method and regularized improved interpolating moving least-square method with nonsingular moment matrices

Author

Listed:
  • Wang, Qiao
  • Zhou, Wei
  • Cheng, Yonggang
  • Ma, Gang
  • Chang, Xiaolin
  • Miao, Yu
  • Chen, E

Abstract

The moving least-square (MLS) method has been popular applied in surface construction and meshless methods. However, the moment matrix in MLS method may be singular for ill quality point sets and the computation of the inverse of the singular moment matrix is difficult. To overcome this problem, a regularized moving least-square method with nonsingular moment matrix is proposed. The shape functions obtained from the regularized MLS method still do not have the delta function property and may result in difficulty for imposing boundary conditions in regularized MLS based meshless method. To overcome this problem, a regularized improved interpolating moving least-square (IIMLS) method based on the IIMLS method is also proposed. Compared with the regularized MLS method, the regularized IIMLS not only has nonsingular moment matrices, but also obtains shape functions with delta function property. Shape functions of the proposed methods are compared in 1D and 2D cases, and the methods have been applied in curve fitting, surface fitting and meshless method in numerical examples.

Suggested Citation

  • Wang, Qiao & Zhou, Wei & Cheng, Yonggang & Ma, Gang & Chang, Xiaolin & Miao, Yu & Chen, E, 2018. "Regularized moving least-square method and regularized improved interpolating moving least-square method with nonsingular moment matrices," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 120-145.
    • Handle: RePEc:eee:apmaco:v:325:y:2018:i:c:p:120-145
    DOI: 10.1016/j.amc.2017.12.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317308767
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.12.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Joldes, Grand Roman & Chowdhury, Habibullah Amin & Wittek, Adam & Doyle, Barry & Miller, Karol, 2015. "Modified moving least squares with polynomial bases for scattered data approximation," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 893-902.
    2. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    3. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhang, Yuanjian & Huang, Yanjun & Chen, Haibo & Na, Xiaoxiang & Chen, Zheng & Liu, Yonggang, 2021. "Driving behavior oriented torque demand regulation for electric vehicles with single pedal driving," Energy, Elsevier, vol. 228(C).
    2. Sun, Fengxin & Wang, Jufeng & Xu, Ying, 2024. "An improved stabilized element-free Galerkin method for solving steady Stokes flow problems," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    3. Wang, Qiao & Zhou, Wei & Feng, Y.T. & Ma, Gang & Cheng, Yonggang & Chang, Xiaolin, 2019. "An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 347-370.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Qiao & Zhou, Wei & Feng, Y.T. & Ma, Gang & Cheng, Yonggang & Chang, Xiaolin, 2019. "An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 347-370.
    2. Joseph Hadaya & Arjun Verma & Yas Sanaiha & Ramin Ramezani & Nida Qadir & Peyman Benharash, 2022. "Machine learning-based modeling of acute respiratory failure following emergency general surgery operations," PLOS ONE, Public Library of Science, vol. 17(4), pages 1-13, April.
    3. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    4. Hauzenberger, Niko & Huber, Florian & Klieber, Karin & Marcellino, Massimiliano, 2025. "Bayesian neural networks for macroeconomic analysis," Journal of Econometrics, Elsevier, vol. 249(PC).
    5. Oxana Babecka Kucharcukova & Jan Bruha, 2016. "Nowcasting the Czech Trade Balance," Working Papers 2016/11, Czech National Bank, Research and Statistics Department.
    6. Carstensen, Kai & Heinrich, Markus & Reif, Magnus & Wolters, Maik H., 2020. "Predicting ordinary and severe recessions with a three-state Markov-switching dynamic factor model," International Journal of Forecasting, Elsevier, vol. 36(3), pages 829-850.
    7. Hou-Tai Chang & Ping-Huai Wang & Wei-Fang Chen & Chen-Ju Lin, 2022. "Risk Assessment of Early Lung Cancer with LDCT and Health Examinations," IJERPH, MDPI, vol. 19(8), pages 1-12, April.
    8. Margherita Giuzio, 2017. "Genetic algorithm versus classical methods in sparse index tracking," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 243-256, November.
    9. Nicolaj N. Mühlbach, 2020. "Tree-based Synthetic Control Methods: Consequences of moving the US Embassy," CREATES Research Papers 2020-04, Department of Economics and Business Economics, Aarhus University.
    10. Adam N. Smith & Stephan Seiler & Ishant Aggarwal, 2023. "Optimal Price Targeting," Marketing Science, INFORMS, vol. 42(3), pages 476-499, May.
    11. Mert Demirer & Francis X. Diebold & Laura Liu & Kamil Yilmaz, 2018. "Estimating global bank network connectedness," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(1), pages 1-15, January.
    12. Wang, Tao & Zhu, Lixing, 2013. "Sparse sufficient dimension reduction using optimal scoring," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 223-232.
    13. Rehim Kılıç, 2025. "Linear and nonlinear econometric models against machine learning models: realized volatility prediction," Finance and Economics Discussion Series 2025-061, Board of Governors of the Federal Reserve System (U.S.).
    14. Dmitriy Drusvyatskiy & Adrian S. Lewis, 2018. "Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 919-948, August.
    15. repec:plo:pone00:0213569 is not listed on IDEAS
    16. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.
    17. Lucian Belascu & Alexandra Horobet & Georgiana Vrinceanu & Consuela Popescu, 2021. "Performance Dissimilarities in European Union Manufacturing: The Effect of Ownership and Technological Intensity," Sustainability, MDPI, vol. 13(18), pages 1-19, September.
    18. Marie Bessec, 2013. "Short‐Term Forecasts of French GDP: A Dynamic Factor Model with Targeted Predictors," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(6), pages 500-511, September.
    19. Ardyn Nordstrom, 2021. "Can Interventions Targeting Community Attitudes Improve Education for Marginalized Students? Evidence from a Mixed-Methods Experimental Design in Zimbabwe," Working Paper 1472, Economics Department, Queen's University.
    20. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2013. "A Survey of L1 Regression," International Statistical Review, International Statistical Institute, vol. 81(3), pages 361-387, December.
    21. Luis Fernando Melo-Velandia & Juan J. Ospina-Tejeiro & Julian A. Parra-Polania, 2020. "Effects of Banco de la Republica’s Communication on the Yield Curve," Borradores de Economia 1137, Banco de la Republica de Colombia.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:325:y:2018:i:c:p:120-145. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.