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2005•Journal of Shaanxi Normal UniversityRequires access

New expressions and fast algorithms for inverse of Hankel matrix and Vandermonde matrix

YE Zheng-lin

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Abstract

The Hankel(Vandermonde)matrix is invertible if systems of Hankel(Vandermonde)equations are solvable. Also, the inversion of a Hankel(Vandermonde)matrix can be denoted as a sum of products of particular matrices. Especially, a fast algorithm for the inversion of a Hankel matrix with O( n~2) operations (rather than O(n~3), as required by standard matrix inversion methods) is derived.

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The Hankel(Vandermonde)matrix is invertible if systems of Hankel(Vandermonde)equations are solvable. Also, the inversion of a Hankel(Vandermonde)matrix can be denoted as a sum of products of particular matrices. Especially, a fast algorithm for the inversion of a Hankel matrix with O( n~2) operations (rather than O(n~3), as required by standard matrix inversion methods) is derived.

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Available abstract

The Hankel(Vandermonde)matrix is invertible if systems of Hankel(Vandermonde)equations are solvable. Also, the inversion of a Hankel(Vandermonde)matrix can be denoted as a sum of products of particular matrices. Especially, a fast algorithm for the inversion of a Hankel matrix with O( n~2) operations (rather than O(n~3), as required by standard matrix inversion methods) is derived.

Key concepts: Vandermonde matrix, Invertible matrix, Hankel matrix, Mathematics, Inversion (geology), Matrix (chemical analysis), Inverse, Single-entry matrix

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