Soft Computing

, Volume 22, Issue 14, pp 4811–4818 | Cite as

Solving fully interval linear systems of equations using tolerable solution criteria

  • P. Karunakar
  • S. Chakraverty
Methodologies and Application


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.


Fully interval linear systems Tolerable solution Center solution Gradient 



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.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Abolmasoumi S, Alavi M (2014) A method for calculating interval linear system. J Math Comput Sci 8(3):193–204Google Scholar
  2. Allahdadi M, Khorram Z (2015) Solving interval linear equations with modified interval arithmetic. Br J Math Comput Sci 10(2):1–8CrossRefGoogle Scholar
  3. Allahviranloo T, Ghanbari M (2012) A new approach to obtain algebraic solution of interval linear systems. Soft Comput 16:121–133CrossRefMATHGoogle Scholar
  4. Beaumont O (1998) Solving interval linear systems with linear programming techniques. Linear Algebra Appl 281(1):293–309MathSciNetCrossRefMATHGoogle Scholar
  5. Behera D, Chakraverty S (2012) A new method for solving real and complex fuzzy system of linear equations. Comput Math Modelling 23(4):507–518MathSciNetCrossRefMATHGoogle Scholar
  6. Bhat RB, Chakraverty S (2007) Numerical analysis in engineering. Alpha Science International Ltd, OxfordGoogle Scholar
  7. Das S, Chakraverty S (2012) Numerical solution of interval and fuzzy system of linear equations. Appl Appl Math 7(1):334–356MathSciNetMATHGoogle Scholar
  8. Dehghan M, Hashemi B (2006) Solution of the fully fuzzy linear systems using the decomposition procedure. Appl Math Comput 182(2):1568–1580MathSciNetMATHGoogle Scholar
  9. Gerald CF, Wheatley PO (2009) Applied numerical analysis. Dorling Kindersley Pvt Ltd, NoidaMATHGoogle Scholar
  10. Hansen ER (1992) Bounding the solution of interval equations. SIAM J Numer Anal 29(5):1493–1503MathSciNetCrossRefMATHGoogle Scholar
  11. Kolev LV (2004) A method for outer interval solution of linear parametric systems. Reliable Comput 10(3):227–239MathSciNetCrossRefMATHGoogle Scholar
  12. Krämer W (2007) Computing and visualizing solution sets of interval linear systems. Serdica J Comput 1(4):455–468MathSciNetMATHGoogle Scholar
  13. Li T, Wel L, Qin W (2013) Tolerance—control solution to interval linear equations. In: International conference on artificial intelligence and software engineeringGoogle Scholar
  14. Moore RE, Kearfott RB, Cloud MJ (2009) Introduction to interval analysis. SIAM Publications, PhiladelphiaCrossRefMATHGoogle Scholar
  15. Nayak S, Chakraverty S (2013) A new approach to solve fuzzy system of linear equations. J Math Comput Sci 7(3):205–212Google Scholar
  16. Neumaier A (1990) Interval methods for systems of equations. Cambridge University Press, CambridgeMATHGoogle Scholar
  17. Ning S, Kearfort RB (1997) A comparison of some methods for soling linear interval equations. SIAM J Numer Anal 34(4):1289–1305MathSciNetCrossRefGoogle Scholar
  18. Rohn J, Farhadsefat R (2011) Inverse interval matrix: a survey. Electr J Linear Algebra 22(1):704–719MathSciNetMATHGoogle Scholar
  19. Shary SP (2002) A new technique in systems analysis under interval uncertainty and ambiguity. Reliable Comput 8(5):321–418MathSciNetCrossRefMATHGoogle Scholar
  20. Shary SP (1995) Solving the linear interval tolerance problem. Math Comput Simul 39(1):53–85MathSciNetCrossRefGoogle Scholar
  21. Skalna I (2003) Methods for solving systems of linear equations of structure mechanics with interval parameters. Comput Assist Mech Eng Sci 10(3):281–293MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of Technology RourkelaRourkelaIndia

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