A novel linear algebra-based method for complex interval linear systems in circuit analysis

Abstract

In this paper, systems of multivariate interval linear equations with complex interval coefficients are examined, and a novel linear algebra-based approach for locating all of their solutions is proposed. The key concept is to convert the system into a crisp polynomial system that is equivalent and allows for the use of the innovative computational features of Gröbner bases. It is possible to calculate all of the system's precise solutions at once after an appropriate Gröbner basis has been determined. Design is a condition for the presence of a solution in complex interval linear systems. In addition, an algorithm is devised to retrieve all solutions using the eigenvalue approach. In addition, a proportional case is solved using the provided approach to demonstrate its efficiency and efficacy. The given approach can locate all solutions for linear systems with complex intervals. Additionally, it determines the presence or absence of a solution for the system. We use the aforementioned technique in the context of circuit analysis to demonstrate the effectiveness of the findings obtained.

Keywords

• Interval analysis
• Eigenvalue method
• Gröbner basis
• Affine variety
• Complex intervals