Vandermonde matrices inversion via synthetic division / Muhammad Aiman Wafi Nazri, Wan Muhammad Sirhan Razali and Nur Khairani Izzati Abdul Kadir

Vandermonde matrix (VDM) research has covered a wide range of topics, including polynomial interpolation, numerical analysis, signal processing, and many others. Vandermonde matrices are a fundamental concept in applied mathematics, natural science, and engineering. The VDM’s inverse form is one of its most important features. Methods for inverting VDM involved multiplying two matrices, such as a product of triangular matrices, computing the determinant and cofactor matrices, and elementary row operations to determine the elements of the inverse of VDM. These techniques, however, have a high computational cost. As a result, this project investigates another approach known as the Synthetic Division method. In this study, the objective is to develop the algorithm of the inverse of VDM by Synthetic Division method in Python programming language. Furthermore, is to analyze the effectiveness and time computation by Synthetic Division method and function numpy.linalg.inv() in the Python NumPy module for the computation of the inverse of VDM and last is to demonstrate the application of the inverse of VDM. To compute the elements of the inverse of VDM, the method uses arithmetic operations, multiplications, and additions.