Skip to main content

Effective Algebraic Methods are Widely Applicable

  • Conference paper
  • First Online:
Proceedings of the Sixth International Conference on Mathematics and Computing

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1262))

  • 284 Accesses

Abstract

This presentation deals with some algebraic methods for mathematical analysis. The main point of using these tools is the ’effectiveness’ of them, where an effective method means that it is a step-by-step procedure (i.e. an algorithm) and the result will be obtained in a finite number of steps. We will study several effective algebraic procedures and explore the fact that they can be used in many applications.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Amitsur A, Levitzki J (1950) Proc Amer Math Soc 1(4):449–463

    Google Scholar 

  2. Eriksso O, Tegnér J (2016) Modeling and model simplification to facilitate biological insights and predictions. In: Geri L, Gomez-Cabrero D (eds.), Uncertainty in biology: a computational modeling approach. Springer, pp. 301–325

    Google Scholar 

  3. Farenick D (2012) Algebras of linear transformations. Springer

    Google Scholar 

  4. Gil M (2001) Linear Algebra Appl 327:95–104

    Google Scholar 

  5. Gil M (2003) Operator functions and localization of spectra. Springer

    Google Scholar 

  6. Jamiołkowski A (2019) On classification of roots of polynomial parametric systems. Lecture at Tokyo University of Science

    Google Scholar 

  7. Jamiołkowski A, Pastuszak G (2015) Linear Multilinear Algebra 63:314–325

    Google Scholar 

  8. Jones DS, Plank M, Sleeman BD (2009) Differential equations and mathematical biology. CRC

    Google Scholar 

  9. Kamizawa T (2017) Open Syst Inf Dyn 24(01):1750002

    Google Scholar 

  10. Kamizawa T (2018) Int J Theor Phys 57(5):1272–1284

    Google Scholar 

  11. Kamizawa T (2019) Algebraic and Lyapunov reducibilities and the analysis of linear dynamical systems and quantum systems. In: Proceedings of mathematical society japan 58th joint symposium of real analysis and functional analysis sections

    Google Scholar 

  12. Laffey TJ (1986) Linear Algebra Appl 84:123–138

    Google Scholar 

  13. Marcus M, Minc H (1992) A survey of matrix theory and matrix inequalities. Courier Corporation

    Google Scholar 

  14. Mitropolsky YA, Lopatin A (2013) Nonlinear mechanics, groups and symmetry. Springer

    Google Scholar 

  15. Pastuszak G, Kamizawa T, Jamiołkowski A (2016) Open Syst Inf Dyn 23:1650003

    Google Scholar 

  16. Saez-Rodriguez J, Kremling A, Conzelmann H, Bettenbrock K, Gilles E (2004) IEEE Control Syst Mag 24(4):35–52

    Google Scholar 

  17. Shapiro J (1979) Linear Algebra Appl 25:129–137

    Google Scholar 

  18. Shemesh D (1984) Linear Algebra Appl 62:11–18

    Google Scholar 

  19. Walter W (1998) Ordinary differential equations. Springer

    Google Scholar 

  20. Xia B, Yang L (2016) Automated inequality proving and discovering. World Scientific

    Google Scholar 

  21. Yang L, Xia B (1997) Explicit criterion to determine the number of positive roots of a polynomial. MM Res Preprints 15:134–145

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Takeo Kamizawa .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 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

Kamizawa, T. (2021). Effective Algebraic Methods are Widely Applicable. In: Giri, D., Buyya, R., Ponnusamy, S., De, D., Adamatzky, A., Abawajy, J.H. (eds) Proceedings of the Sixth International Conference on Mathematics and Computing. Advances in Intelligent Systems and Computing, vol 1262. Springer, Singapore. https://doi.org/10.1007/978-981-15-8061-1_42

Download citation

Publish with us

Policies and ethics