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

Chakraverty S., Hladík M., Mahato N. R.

Fundamenta Informaticae

2017

Vol. 152, nr 1

13--31

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.

Enclosures for the solution set of parametric interval linear systems

Hladík M.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 3

561-574

We investigate parametric interval linear systems of equations. The main result is a generalization of the Bauer-Skeel and the Hansen-Bliek-Rohn bounds for this case, comparing and refinement of both. We show that the latter bounds are not provable better, and that they are also sometimes too pessimistic. The presented form of both methods is suitable for combining them into one to get a more efficient algorithm. Some numerical experiments are carried out to illustrate performances of the methods.