A New Derivation and Recursive Algorithm Based on Wronskian Matrix for Vandermonde Inverse Matrix

Abstract

For an analytical expression of Vandermonde inverse matrix, a new derivation process based on Wronskian matrix and Lagrange interpolation polynomial basis is presented. Recursive formula and implementation cases for the direct formula of Vandermonde inverse matrix are given based on deriving the unified formula of Wronskian inverse matrix. For the calculation of symbol-type Vandermonde inverse matrix, the direct formula and recursive method are verified to be more efficient than Mathematica which is good at symbolic computation by comparing the computing time in Mathematica. The process and steps of recursive algorithm are relatively simple. The derivation process and idea both have very important values in theory and practice of Vandermonde and generalized Vandermonde inverse matrix.

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

“…In recent decades, there have been many fruitful research papers for computing the inverse of the classical Vandermonde matrix using different approaches. The interested reader may refer to [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In an article by El Mikkawy [21], an explicit formula for the inverse of a generalized Vandermonde matrix was given, which was proved from the inverse of a classical Vandermonde matrix, while, in this article, we provide another proof for that formula.…”