Skip to main content
SpringerLink
Log in

Adaptive Wavelet Decomposition of Matrix Flows

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Adaptive algorithms for constructing spline-wavelet decompositions of matrix flows from a linear space of matrices over a normed field are presented. The algorithms suggested provides for an a priori prescribed estimate of the deviation of the basic flow from the initial one. Comparative bounds of the volumes of data in the basic flow for various irregularity characteristics of the initial flow are obtained in the cases of pseudo-equidistant and adaptive grids. Limit characteristics of the above-mentioned volumes are given in the cases where the initial flow is generated by differentiable functions.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Blahut, Fast Algorithms for Digital Signal Processing, Addison-Wesley Publishing Company (1989).

  2. S. Mallat, A Wavelet Tour of Signal Processing, Academic Press (1999).

  3. I. Y. Novikov, V. Y. Protasov, and M. A. Skopina, Theory of Wavelets [in Russian], Fizmatlit, Moscow (2005).

  4. Yu. K. Dem’yanovich, Theory of Spline-Wavelets [in Russian], St.Petersburg State University (2013).

  5. S. Albeverio, S. Evdokimov, and M. Skopina, “p-adic multiresolution analysis and wavelet frames,” J. Fourier Anal. Appl., 16, No. 5, 693–714 (2010).

  6. Yu. K. Dem’yanovich and A. Yu. Ponomareva, “Adaptive spline-wavelet processing of a discrete flow,” Probl. Mat. Anal., 81, 29–46 (2015).

  7. Yu. K. Dem’yanovich and A. S. Ponomarev, “On realization of the spline-wavelet decomposition of the first order,” Zap. Nauchn. Semin. POMI, 453, 33–73 (2016).

  8. Yu. K. Dem’yanovich, “On embedding and extended smoothness of spline spaces,” Far East J. Math. Sci. (FJMS), 102, No. 9, 2025–2052 (2017).

Download references

Author information

Authors and Affiliations

  1. St.Petersburg State University, St.Petersburg, Russia

    Yu. K. Dem’yanovich & N. A. Lebedinskaya

  2. Emperor Alexander I St.Petersburg State Transport University, St.Petersburg, Russia

    V. G. Degtyarev

Authors
  1. Yu. K. Dem’yanovich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. G. Degtyarev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. A. Lebedinskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. K. Dem’yanovich.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 463, 2017, pp. 112–131.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dem’yanovich, Y.K., Degtyarev, V.G. & Lebedinskaya, N.A. Adaptive Wavelet Decomposition of Matrix Flows. J Math Sci 232, 816–829 (2018). https://doi.org/10.1007/s10958-018-3911-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-018-3911-0

Search

Navigation