Interval System of Linear Equations

Abstract

Differential equations serve as the backbone of various science and engineering problems viz. structure analysis, control theory, image processing, circuit analysis, robotics, etc. and there exist variety of methods for solving such differential equations. Generally, under static conditions, the governing differential equations get converted to system of equations. But in actual practice, as a result of errors in measurements, observations, calculations, or due to maintenance induced errors, etc., the differential equations and the corresponding system of equations have uncertain parameters that may be handled using probabilistic approach, interval analysis, and fuzzy set theory. Unfortunately, the probabilistic approach may not deliver reliable results at the required precision without sufficient experimental data. As such, interval analysis and fuzzy set theory serve as powerful tools for handling uncertain parameters or values having infimum and supremum. In Chap. 1, the notion of interval matrix has been introduced and as such, this chapter deals with application of interval matrices for solving interval system of linear equations (ISLEs). Further, the chapter includes certain solved numerical examples along with MATLAB codes and also consists of few unsolved problems for self-evaluation.