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For an analytical expression of Vandermonde inverse matrix, a new derivation process basedon Wronskian matrix and Lagrange interpolation polynomial basis is presented. Recursiveformula and implementation cases for the direct formula of Vandermonde inverse matrix aregiven based on deriving the unified formula of Wronskian inverse matrix. For the calculation ofsymbol-type Vandermonde inverse matrix, the direct formula and recursive method are verifiedto be more efficient than Mathematica which is good at symbolic computation by comparingthe computing time in Mathematica. The process and steps of recursive algorithm are relativelysimple. The derivation process and idea both have very important values in theory and practiceof Vandermonde and generalized Vandermonde inverse matrix.

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