IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i7p1012-d776614.html
   My bibliography  Save this article

An Iterative Algorithm for Approximating the Fixed Point of a Contractive Affine Operator

Author

Listed:
  • María Isabel Berenguer

    (Department of Applied Mathematics, E.T.S. Ingeniería de Edificación, University of Granada, 18071 Granada, Spain
    Institute of Mathematics (IMAG), University of Granada, 18071 Granada, Spain
    These authors contributed equally to this work.)

  • Manuel Ruiz Galán

    (Department of Applied Mathematics, E.T.S. Ingeniería de Edificación, University of Granada, 18071 Granada, Spain
    Institute of Mathematics (IMAG), University of Granada, 18071 Granada, Spain
    These authors contributed equally to this work.)

Abstract

First of all, in this paper we obtain a perturbed version of the geometric series theorem, which allows us to present an iterative numerical method to approximate the fixed point of a contractive affine operator. This result requires some approximations that we obtain using the projections associated with certain Schauder bases. Next, an algorithm is designed to approximate the solution of Fredholm’s linear integral equation, and we illustrate the behavior of the method with some numerical examples.

Suggested Citation

  • María Isabel Berenguer & Manuel Ruiz Galán, 2022. "An Iterative Algorithm for Approximating the Fixed Point of a Contractive Affine Operator," Mathematics, MDPI, vol. 10(7), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1012-:d:776614
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/7/1012/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/7/1012/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Karimi, Saeed & Jozi, Meisam, 2015. "A new iterative method for solving linear Fredholm integral equations using the least squares method," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 744-758.
    2. Yonghong Yao & Mihai Postolache & Jen-Chih Yao, 2019. "An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems," Mathematics, MDPI, vol. 7(1), pages 1-15, January.
    3. Cominola, A. & Giuliani, M. & Piga, D. & Castelletti, A. & Rizzoli, A.E., 2017. "A Hybrid Signature-based Iterative Disaggregation algorithm for Non-Intrusive Load Monitoring," Applied Energy, Elsevier, vol. 185(P1), pages 331-344.
    4. S. Saha Ray & P. K. Sahu, 2013. "Numerical Methods for Solving Fredholm Integral Equations of Second Kind," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-17, December.
    5. Alipour, Sahar & Mirzaee, Farshid, 2020. "An iterative algorithm for solving two dimensional nonlinear stochastic integral equations: A combined successive approximations method with bilinear spline interpolation," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    Full references (including those not matched with items on IDEAS)

    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. Shi, Xin & Ming, Hao & Shakkottai, Srinivas & Xie, Le & Yao, Jianguo, 2019. "Nonintrusive load monitoring in residential households with low-resolution data," Applied Energy, Elsevier, vol. 252(C), pages 1-1.
    2. Himeur, Yassine & Alsalemi, Abdullah & Bensaali, Faycal & Amira, Abbes, 2020. "Effective non-intrusive load monitoring of buildings based on a novel multi-descriptor fusion with dimensionality reduction," Applied Energy, Elsevier, vol. 279(C).
    3. Moreno Jaramillo, Andres F. & Laverty, David M. & Morrow, D. John & Martinez del Rincon, Jesús & Foley, Aoife M., 2021. "Load modelling and non-intrusive load monitoring to integrate distributed energy resources in low and medium voltage networks," Renewable Energy, Elsevier, vol. 179(C), pages 445-466.
    4. Ce Peng & Guoying Lin & Shaopeng Zhai & Yi Ding & Guangyu He, 2020. "Non-Intrusive Load Monitoring via Deep Learning Based User Model and Appliance Group Model," Energies, MDPI, vol. 13(21), pages 1-19, October.
    5. Qian Wu & Fei Wang, 2019. "Concatenate Convolutional Neural Networks for Non-Intrusive Load Monitoring across Complex Background," Energies, MDPI, vol. 12(8), pages 1-17, April.
    6. Song, Chunhe & Jing, Wei & Zeng, Peng & Yu, Haibin & Rosenberg, Catherine, 2018. "Energy consumption analysis of residential swimming pools for peak load shaving," Applied Energy, Elsevier, vol. 220(C), pages 176-191.
    7. Yini Ni & Yanghong Xia & Zichen Li & Qifan Feng, 2023. "A Non-Intrusive Identification Approach for Residential Photovoltaic Systems Using Transient Features and TCN with Attention Mechanisms," Sustainability, MDPI, vol. 15(20), pages 1-22, October.
    8. Jiang, Zhanhong & Liu, Chao & Akintayo, Adedotun & Henze, Gregor P. & Sarkar, Soumik, 2017. "Energy prediction using spatiotemporal pattern networks," Applied Energy, Elsevier, vol. 206(C), pages 1022-1039.
    9. Anthony Faustine & Lucas Pereira, 2020. "Improved Appliance Classification in Non-Intrusive Load Monitoring Using Weighted Recurrence Graph and Convolutional Neural Networks," Energies, MDPI, vol. 13(13), pages 1-15, July.
    10. Arvind Kumar Rajpoot & Mohd Ishtyak & Rais Ahmad & Yuanheng Wang & Jen-Chih Yao, 2023. "Convergence Analysis for Yosida Variational Inclusion Problem with Its Corresponding Yosida Resolvent Equation Problem through Inertial Extrapolation Scheme," Mathematics, MDPI, vol. 11(3), pages 1-19, February.
    11. Wen, Xiaoxia & Huang, Jin, 2021. "A combination method for numerical solution of the nonlinear stochastic Itô-Volterra integral equation," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    12. Yan, Lei & Tian, Wei & Han, Jiayu & Li, Zuy, 2022. "Event-driven two-stage solution to non-intrusive load monitoring," Applied Energy, Elsevier, vol. 311(C).
    13. Ahir, Rajesh K. & Chakraborty, Basab, 2021. "A meta-analytic approach for determining the success factors for energy conservation," Energy, Elsevier, vol. 230(C).
    14. Dinesh, Chinthaka & Welikala, Shirantha & Liyanage, Yasitha & Ekanayake, Mervyn Parakrama B. & Godaliyadda, Roshan Indika & Ekanayake, Janaka, 2017. "Non-intrusive load monitoring under residential solar power influx," Applied Energy, Elsevier, vol. 205(C), pages 1068-1080.
    15. Hwan Kim & Sungsu Lim, 2021. "Temporal Patternization of Power Signatures for Appliance Classification in NILM," Energies, MDPI, vol. 14(10), pages 1-17, May.
    16. Welikala, Shirantha & Thelasingha, Neelanga & Akram, Muhammed & Ekanayake, Parakrama B. & Godaliyadda, Roshan I. & Ekanayake, Janaka B., 2019. "Implementation of a robust real-time non-intrusive load monitoring solution," Applied Energy, Elsevier, vol. 238(C), pages 1519-1529.
    17. Sara Tavakoli & Kaveh Khalilpour, 2021. "A Practical Load Disaggregation Approach for Monitoring Industrial Users Demand with Limited Data Availability," Energies, MDPI, vol. 14(16), pages 1-27, August.
    18. Bisaga, Iwona & Puźniak-Holford, Nathan & Grealish, Ashley & Baker-Brian, Christopher & Parikh, Priti, 2017. "Scalable off-grid energy services enabled by IoT: A case study of BBOXX SMART Solar," Energy Policy, Elsevier, vol. 109(C), pages 199-207.
    19. Liu, Yu & Liu, Wei & Shen, Yiwen & Zhao, Xin & Gao, Shan, 2021. "Toward smart energy user: Real time non-intrusive load monitoring with simultaneous switching operations," Applied Energy, Elsevier, vol. 287(C).
    20. Ahmadinia, M. & Afshariarjmand, H. & Salehi, M., 2023. "Numerical solution of multi-dimensional Itô Volterra integral equations by the second kind Chebyshev wavelets and parallel computing process," Applied Mathematics and Computation, Elsevier, vol. 450(C).

    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:gam:jmathe:v:10:y:2022:i:7:p:1012-:d:776614. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.