Kalpa Publications in Computing Volume 8, 2018, Pages 70–83 TNC’18. Trusted Numerical Computations Enhancing monotonicity checking in parametric interval linear systems Iwona Skalna 1 and Milan Hlad´ ık 2 1 AGH University of Science and Technology, Department of Applied Computer Science, Krak´ ow, Poland skalna@agh.edu.pl 2 Charles University, Faculty of Mathematics and Physics, Department of Applied Mathematics, Malostransk´ e n´ am. 25, 11800, Prague, Czech Republic milan.hladik@matfyz.cz Abstract Solving systems of parametric linear equations with parameters varying within closed intervals is a hard computational problem. However, we may reduce the problem dimension and thus make the problem more tractable by utilizing the monotonicity of the solution components with respect to the parameters. In this paper, we propose two improvements of the standard monotonicity checking techniques. The first improvement relies on creating a system with original variables and their derivatives as unknowns, and the second one employs the so-called p-solution. By a series of numerical experiments we show that the improved monotonicity approach outperforms the standard one. 1 Introduction In solving real-life problems, we often deal with data that are not know exactly due to various kinds of inexactness – measurement errors, incomplete knowledge, data estimation etc. In this paper, we assume that lower and upper bounds on uncertain data are known; i.e., we assume that we are dealing with interval valued quantities. Using intervals is advantageous because of their ability to track rounding and truncation errors and what follows to produce guaranteed solutions. However, due to the so-called dependency problem, classical interval computations often lead to large overestimation which makes their results irrelevant. Therefore, we address here a more general problem with dependencies between interval entries. More specifically, we focus on solving systems of linear equations with entries dependent on parameters varying within prescribed intervals. Formally, consider an n-dimensional system of linear equations A(p)x = b(p), in which the constraint matrix A(p) and the right-hand side vector b(p) depend on parameters p 1 ,...,p K . The parameters are assumed to vary within compact intervals, i.e., for k =1,...,K, M. Martel, N. Damouche and J. Alexandre Dit Sandretto (eds.), TNC’18 (Kalpa Publications in Computing, vol. 8), pp. 70–83