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.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Abolmasoumi S, Alavi M (2014) A method for calculating interval linear system. J Math Comput Sci 8(3):193–204
Allahdadi M, Khorram Z (2015) Solving interval linear equations with modified interval arithmetic. Br J Math Comput Sci 10(2):1–8
Allahviranloo T, Ghanbari M (2012) A new approach to obtain algebraic solution of interval linear systems. Soft Comput 16:121–133
Beaumont O (1998) Solving interval linear systems with linear programming techniques. Linear Algebra Appl 281(1):293–309
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
Bhat RB, Chakraverty S (2007) Numerical analysis in engineering. Alpha Science International Ltd, Oxford
Das S, Chakraverty S (2012) Numerical solution of interval and fuzzy system of linear equations. Appl Appl Math 7(1):334–356
Dehghan M, Hashemi B (2006) Solution of the fully fuzzy linear systems using the decomposition procedure. Appl Math Comput 182(2):1568–1580
Gerald CF, Wheatley PO (2009) Applied numerical analysis. Dorling Kindersley Pvt Ltd, Noida
Hansen ER (1992) Bounding the solution of interval equations. SIAM J Numer Anal 29(5):1493–1503
Kolev LV (2004) A method for outer interval solution of linear parametric systems. Reliable Comput 10(3):227–239
Krämer W (2007) Computing and visualizing solution sets of interval linear systems. Serdica J Comput 1(4):455–468
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
Nayak S, Chakraverty S (2013) A new approach to solve fuzzy system of linear equations. J Math Comput Sci 7(3):205–212
Neumaier A (1990) Interval methods for systems of equations. Cambridge University Press, Cambridge
Ning S, Kearfort RB (1997) A comparison of some methods for soling linear interval equations. SIAM J Numer Anal 34(4):1289–1305
Rohn J, Farhadsefat R (2011) Inverse interval matrix: a survey. Electr J Linear Algebra 22(1):704–719
Shary SP (2002) A new technique in systems analysis under interval uncertainty and ambiguity. Reliable Comput 8(5):321–418
Shary SP (1995) Solving the linear interval tolerance problem. Math Comput Simul 39(1):53–85
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
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
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Communicated by V. Loia.
Rights and permissions
About this article
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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-017-2668-6