Recursive Matrix Calculation Paradigm by the Example of Structured Matrix

Abstract

In this paper, we derive recursive algorithms for calculating the determinant and inverse of the generalized Vandermonde matrix. The main advantage of the recursive algorithms is the fact that the computational complexity of the presented algorithm is better than calculating the determinant and the inverse by means of classical methods, developed for the general matrices. The results of this article do not require any symbolic calculations and, therefore, can be performed by a numerical algorithm implemented in a specialized (like Matlab or Mathematica) or general-purpose programming language (C, C++, Java, Pascal, Fortran, etc.).

A Fast Novel Recursive Algorithm for Computing the Inverse of a Generalized Vandermonde Matrix

“…However, what distinguishes the method in the current paper is the possibility of calculating the inverse of the Vandermonde matrix V n,p via hand calculation and also via computer programming with a computational cost of O(n 2 ). Elementary symmetric polynomial (ESP) is a basic tool in computing the inverse of the Vandermonde matrix V n,p , see for instance [21][22][23][24].…”