Inversion of Vandermonde matrices via synthetic division formulation

• Published in: AIP Conference Proceedings
• Main Author: Ahmad S.N.; Kadir N.K.I.A.; Nazri M.A.W.; Razali W.M.S.
• Format: Conference paper
• Language: English
• Published: American Institute of Physics 2024
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85202643290&doi=10.1063%2f5.0224748&partnerID=40&md5=7b083ee065b593bc7c302a818a903f8f

Vandermonde matrices are fundamental in applied mathematics, natural sciences, and engineering. The inverse form of the Vandermonde matrix (V) is one of its most important characteristics. The purpose of this paper is to develop an algorithm for the inverse of Vandermonde matrix, V-1 in the Python programming language using the Synthetic Division method. To compute the elements of V-1, the Synthetic Division uses arithmetic operations, multiplications, and additions. Consequently, inverse matrix computations require less time compared to a method that involved the multiplication of two matrices. In addition, the efficiency and time required to compute V-1 using Synthetic Division versus the numpy.linalg.inv() function in the Python NumPy module are compared. The study found that the NumPy inverse function demonstrated that the time computation of inverse matrices is consistent, except for certain sizes. In contrast, the Synthetic Division algorithm appears consistent regardless of matrix size. Therefore, Synthetic Division is an effective and efficient method for computing V-1. © 2024 Author(s).