Skip to main content
SpringerLink
Log in

Linear Recurrent Fractal Interpolation Function for Data Set with Gaussian Noise

  • Conference paper
  • First Online:
Mathematics and Computing (ICMC 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 415))

Included in the following conference series:

  • 306 Accesses

Abstract

In this article, we use the linear recurrent fractal interpolation function approach to interpolate a data set with Gaussian noise on its ordinate. To investigate the variability at any intermediate point in the given noisy data set, we estimate the parameters of the probability distribution of the fractal function. In addition, we present a simulation study that experimentally confirms our theoretical findings.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Barnsley, M.F.: Fractal functions and interpolation. Constr. Approx. 2(1), 303–329 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barnsley, M.F., Elton, J.H., Hardin, D.P.: Recurrent iterated function systems. Constr. approx. 5(1), 3–31 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  3. Navascués, M.A.: Fractal polynomial interpolation. Z. Anal. Anwend. 24(2), 401–418 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Massopust, P.R.: Vector-valued fractal interpolation functions and their box dimension. Aequat. Math. 42(1), 1–22 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  5. Massopust, P.R.: Local fractal interpolation on unbounded domains. Proc. Edinb. Math. Soc. 61(1), 151–167 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  6. Buzogány, E., Kolumbán, J., Soós, A.: Random fractal interpolation function using contraction method in probabilistic metric spaces. An. Univ. Bucuresti Mat. Inform. 51(1), 13–24 (2002)

    MathSciNet  MATH  Google Scholar 

  7. Luor, D.C.: Statistical properties of linear fractal interpolation functions for random data sets. Fractals 26(1), 1–6 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  8. Luor, D.C.: Fractal interpolation functions for random data sets. Chaos, Solitons Fractals 114, 256–263 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kumar, M., Upadhye, N.S., Chand, A.K.B.: Distribution of linear fractal interpolation function for random dataset with stable noise. Fractals 29(4), 1–12 (2021)

    Article  MATH  Google Scholar 

  10. Chand, A.K.B., Kapoor, G.P.: Generalized cubic spline fractal interpolation functions. SIAM J. Numer. Anal. 44(2), 655–676 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chand, A.K.B., Viswanathan, P.: A constructive approach to cubic Hermite fractal interpolation function and its constrained aspects. BIT Numer. Math. 53, 841–865 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Navascués, M.A., Sebastián, M.V.: Smooth fractal interpolation. J. Inequal. Appl. 78734, 1–20 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Chand, A.K.B., Kapoor, G.P.: Stability of affine coalescence hidden variable fractal interpolation functions. Nonlinear Anal. Theory Methods Appl. 68(12), 3757–3770 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Viswanathan, P., Chand, A.K.B., Agarwal, R.P.: Preserving convexity through rational cubic spline fractal interpolation function. J. Comput. Appl. Math. 263, 262–276 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Chand, A.K.B., Vijender, N., Agarwal, R.P.: Rational iterated function system for positive/monotonic shape preservation. Adv. Differ. Equ. 2014(30), 1–19 (2014)

    MathSciNet  MATH  Google Scholar 

  16. Chand, A.K.B., Vijender, N., Navascués, M.A.: Shape preservation of scientific data through rational fractal splines. Calcolo 51, 329–362 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. Banerjee, S., Easwaramoorthy, D., Gowrisankar, A.: Fractal Functions Dimensions and Signal Analysis. Springer International Publishing (2021)

    Google Scholar 

  18. Păcurar, C.M., Necula, B.R.: An analysis of COVID-19 spread based on fractal interpolation and fractal dimension. Chaos, Solitons Fractals 139, 1–8 (2020)

    Article  MathSciNet  Google Scholar 

  19. Bajahzar, A., Guedri, H.: Reconstruction of fingerprint shape using fractal interpolation. Int. J. Adv. Comput. Sci. Appl. 10(5), 103–114 (2019)

    Google Scholar 

  20. Barnsley, M.F., Demko, S.: Iterated function systems and the global construction of fractals. Proc. R. Soc. Lond. Ser. A 399(1817), 243–275 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  21. Barnsley, M.F.: Fractals Everywhere. 2nd edn., Morgan Kaufmann (2000)

    Google Scholar 

Download references

Acknowledgements

The authors are thankful for the funding by Indian Institute of Technology Madras under the MHRD Project No.: SB20210848MAMHRD008558.

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600036, Tamil Nadu, India

    Mohit Kumar, Neelesh S. Upadhye & A. K. B. Chand

Authors
  1. Mohit Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Neelesh S. Upadhye
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. K. B. Chand
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohit Kumar .

Editor information

Editors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    B. Rushi Kumar

  2. Department of Mathematics, Indian Institute of Technology Madras, Chennai, Tamil Nadu, India

    S. Ponnusamy

  3. Department of Information Technology, Maulana Abul Kalam Azad University of Technology, Haringhata, West Bengal, India

    Debasis Giri

  4. Department of Computer Science, The University of Texas at Dallas, Richardson, TX, USA

    Bhavani Thuraisingham

  5. Department of Computer Science, Purdue University, West Lafayette, IN, USA

    Christopher W. Clifton

  6. Department of Theoretical and Applied Sciences, University of Insubria, Varese, Italy

    Barbara Carminati

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kumar, M., Upadhye, N.S., Chand, A.K.B. (2022). Linear Recurrent Fractal Interpolation Function for Data Set with Gaussian Noise. In: Rushi Kumar, B., Ponnusamy, S., Giri, D., Thuraisingham, B., Clifton, C.W., Carminati, B. (eds) Mathematics and Computing. ICMC 2022. Springer Proceedings in Mathematics & Statistics, vol 415. Springer, Singapore. https://doi.org/10.1007/978-981-19-9307-7_19

Download citation

Publish with us

Policies and ethics

Search

Navigation