Skip to main content
SpringerLink
Log in

Solving fully interval linear systems of equations using tolerable solution criteria

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

A new method has been proposed here for solving fully interval linear systems of equations where both coefficient matrix and the right-hand side vector are intervals. In this method, center solution has been used with the tolerable solution criteria to compute the inner solution set. A few example problems are solved to demonstrate the proposed method. Numerical results are compared with existing methods and are found to be in good agreement.

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

  • Abolmasoumi S, Alavi M (2014) A method for calculating interval linear system. J Math Comput Sci 8(3):193–204

    Google Scholar 

  • Allahdadi M, Khorram Z (2015) Solving interval linear equations with modified interval arithmetic. Br J Math Comput Sci 10(2):1–8

    Article  Google Scholar 

  • Allahviranloo T, Ghanbari M (2012) A new approach to obtain algebraic solution of interval linear systems. Soft Comput 16:121–133

    Article  MATH  Google Scholar 

  • Beaumont O (1998) Solving interval linear systems with linear programming techniques. Linear Algebra Appl 281(1):293–309

    Article  MathSciNet  MATH  Google Scholar 

  • Behera D, Chakraverty S (2012) A new method for solving real and complex fuzzy system of linear equations. Comput Math Modelling 23(4):507–518

    Article  MathSciNet  MATH  Google Scholar 

  • Bhat RB, Chakraverty S (2007) Numerical analysis in engineering. Alpha Science International Ltd, Oxford

    Google Scholar 

  • Das S, Chakraverty S (2012) Numerical solution of interval and fuzzy system of linear equations. Appl Appl Math 7(1):334–356

    MathSciNet  MATH  Google Scholar 

  • Dehghan M, Hashemi B (2006) Solution of the fully fuzzy linear systems using the decomposition procedure. Appl Math Comput 182(2):1568–1580

    MathSciNet  MATH  Google Scholar 

  • Gerald CF, Wheatley PO (2009) Applied numerical analysis. Dorling Kindersley Pvt Ltd, Noida

    MATH  Google Scholar 

  • Hansen ER (1992) Bounding the solution of interval equations. SIAM J Numer Anal 29(5):1493–1503

    Article  MathSciNet  MATH  Google Scholar 

  • Kolev LV (2004) A method for outer interval solution of linear parametric systems. Reliable Comput 10(3):227–239

    Article  MathSciNet  MATH  Google Scholar 

  • Krämer W (2007) Computing and visualizing solution sets of interval linear systems. Serdica J Comput 1(4):455–468

    MathSciNet  MATH  Google Scholar 

  • Li T, Wel L, Qin W (2013) Tolerance—control solution to interval linear equations. In: International conference on artificial intelligence and software engineering

  • Moore RE, Kearfott RB, Cloud MJ (2009) Introduction to interval analysis. SIAM Publications, Philadelphia

    Book  MATH  Google Scholar 

  • Nayak S, Chakraverty S (2013) A new approach to solve fuzzy system of linear equations. J Math Comput Sci 7(3):205–212

    Google Scholar 

  • Neumaier A (1990) Interval methods for systems of equations. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Ning S, Kearfort RB (1997) A comparison of some methods for soling linear interval equations. SIAM J Numer Anal 34(4):1289–1305

    Article  MathSciNet  Google Scholar 

  • Rohn J, Farhadsefat R (2011) Inverse interval matrix: a survey. Electr J Linear Algebra 22(1):704–719

    MathSciNet  MATH  Google Scholar 

  • Shary SP (2002) A new technique in systems analysis under interval uncertainty and ambiguity. Reliable Comput 8(5):321–418

    Article  MathSciNet  MATH  Google Scholar 

  • Shary SP (1995) Solving the linear interval tolerance problem. Math Comput Simul 39(1):53–85

    Article  MathSciNet  Google Scholar 

  • Skalna I (2003) Methods for solving systems of linear equations of structure mechanics with interval parameters. Comput Assist Mech Eng Sci 10(3):281–293

    MATH  Google Scholar 

Download references

Acknowledgements

The authors are thankful to Board of Research in Nuclear Sciences (BRNS), Mumbai, India, for the support and funding to carry out the present research work. We would like to thank also to anonymous reviewers for their suggestions which have helped in improving the contents of this paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, 769 008, India

    P. Karunakar & S. Chakraverty

Authors
  1. P. Karunakar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Chakraverty
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Chakraverty.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karunakar, P., Chakraverty, S. Solving fully interval linear systems of equations using tolerable solution criteria. Soft Comput 22, 4811–4818 (2018). https://doi.org/10.1007/s00500-017-2668-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-017-2668-6

Keywords

Search

Navigation