A Sign Function Approach to Solve Algebraically Interval System of Linear Equations for Nonnegative Solutions

This paper deals with solving interval system of linear equations. The problem is to find a nonnegative algebraic solution. Based on sign function approach and using interval center and radius arithmetic operations, we propose an algorithm for computation of an algebraic interval solution vector. We also discuss fundamental properties of this solution vector, such as existence and uniqueness. Further, the nonnegative solution algorithm has been extended to other signrestricted approach. Numerical examples of interval system of linear equations show efficiency of the algorithms presented. ∗Address for correspondence: Department of Mathematics, National Institute of Technology Rourkela, Odisha, India. Received April 2016; revised December 2016. 14 S. Chakraverty et al. / Nonnegative Solutions for Interval System of Equations

[1]  Anatoly V. Lakeyev,et al.  On the computational complexity of the solution of linear systems with moduli , 1996, Reliab. Comput..

[2]  Tofigh Allahviranloo,et al.  A new approach to obtain algebraic solution of interval linear systems , 2012, Soft Comput..

[3]  J. Rohn.  Systems of linear interval equations , 1989 .

[4]  R. B. Kearfott,et al.  A Comparison of some Methods for Solving Linear Interval Equations , 1997 .

[5]  Evgenija D. Popova,et al.  Parametric Interval Linear Solver , 2004, Numerical Algorithms.

[6]  Sergey P. Shary,et al.  A New Technique in Systems Analysis Under Interval Uncertainty and Ambiguity , 2002, Reliab. Comput..

[7]  Milan Hladík,et al.  A Shaving Method for Interval Linear Systems of Equations , 2013, PPAM.

[8]  A. Neumaier.  Interval methods for systems of equations , 1990 .

[9]  Milan Hladík,et al.  Enclosures for the solution set of parametric interval linear systems , 2012, Int. J. Appl. Math. Comput. Sci..

[10]  Snehashish Chakraverty,et al.  Fuzzy Analysis of Structures with Imprecisely DefinedProperties , 2013 .

[11]  Mehdi Dehghan,et al.  Computational methods for solving fully fuzzy linear systems , 2006, Appl. Math. Comput..

[12]  Arnold Neumaier,et al.  Linear Interval Equations , 1986, Interval Mathematics.

[13]  R. Baker Kearfott,et al.  Introduction to Interval Analysis , 2009 .

[14]  H. Carter.  Fuzzy Sets and Systems — Theory and Applications , 1982 .

[15]  I. Elishakoff,et al.  Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis , 1998 .

[16]  S. Chakraverty,et al.  New approach to solve fully fuzzy system of linear equations using single and double parametric form of fuzzy numbers , 2015 .

[17]  Evgenija D. Popova,et al.  Visualizing parametric solution sets , 2008 .

[18]  S. Mcwilliam.  Anti-optimisation of uncertain structures using interval analysis , 2001 .

[19]  G. Alefeld,et al.  Introduction to Interval Computation , 1983 .

[20]  Evgenija D. Popova,et al.  Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm , 2022 .

[21]  M. Hladík,et al.  Formal solution of an interval system of linear equations with an application in static responses of structures with interval forces , 2017 .

[22]  Hadi Sadoghi Yazdi,et al.  Fuzzy Complex System of Linear EquationsApplied to Circuit Analysis , 2009, International Journal of Computer and Electrical Engineering.

[23]  Snehashish Chakraverty,et al.  Numerical solution of interval and fuzzy system of linear equations , 2011 .