Interval Iterative Decreasing Dimension Method for Interval Linear Systems and Its Implementation to Analog Circuits

Abstract

The iterative decreasing dimension method (IDDM) is an iterative method used to solve the linear algebraic system Ax=f. Such systems are important in modeling many problems in applied sciences. For a number of reasons, such as estimated measurements made for modeling, errors arising from floating point calculations, and approximation methods used for solutions, it becomes necessary to study intervals in the solutions of systems of linear equations. The objective of this paper is to utilize IDDM to achieve resolution in the interval linear system (ILS). During the calculations, the Kaucher space is considered an extended classical interval space. The solutions of Barth-Nuding and Hansen interval linear systems, which are commonly used in the literature to test the solutions of ILSs, are obtained with the interval iterative decreasing dimension method for interval linear systems (I-IDDM). Since IDDM is a variation method of Gaussian elimination, a comparative analysis of the results with the interval Gaussian elimination method (I-GEM) is performed. It has been demonstrated that our approach, I-IDDM, produces better outcomes than I-GEM. I-IDDM is also used to investigate the analog circuit problem, where interval analysis is crucial.