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

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

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 uni...

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Main Authors: Qun Zhou, Xinjian Zhang, Xiongwei Liu
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2015/924757
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spelling doaj-fc1eaa670b094460bbce990f0ccd660a2020-11-24T21:54:24ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/924757924757A New Derivation and Recursive Algorithm Based on Wronskian Matrix for Vandermonde Inverse MatrixQun Zhou0Xinjian Zhang1Xiongwei Liu2School of Information Science and Engineering, Hunan International Economics University, Changsha, Hunan 410205, ChinaCollege of Science, National University of Defense Technology, Changsha, Hunan 410073, ChinaCollege of Science, National University of Defense Technology, Changsha, Hunan 410073, ChinaFor 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.http://dx.doi.org/10.1155/2015/924757
collection DOAJ
language English
format Article
sources DOAJ
author Qun Zhou
Xinjian Zhang
Xiongwei Liu
spellingShingle Qun Zhou
Xinjian Zhang
Xiongwei Liu
A New Derivation and Recursive Algorithm Based on Wronskian Matrix for Vandermonde Inverse Matrix
Mathematical Problems in Engineering
author_facet Qun Zhou
Xinjian Zhang
Xiongwei Liu
author_sort Qun Zhou
title A New Derivation and Recursive Algorithm Based on Wronskian Matrix for Vandermonde Inverse Matrix
title_short A New Derivation and Recursive Algorithm Based on Wronskian Matrix for Vandermonde Inverse Matrix
title_full A New Derivation and Recursive Algorithm Based on Wronskian Matrix for Vandermonde Inverse Matrix
title_fullStr A New Derivation and Recursive Algorithm Based on Wronskian Matrix for Vandermonde Inverse Matrix
title_full_unstemmed A New Derivation and Recursive Algorithm Based on Wronskian Matrix for Vandermonde Inverse Matrix
title_sort new derivation and recursive algorithm based on wronskian matrix for vandermonde inverse matrix
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2015-01-01
description 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.
url http://dx.doi.org/10.1155/2015/924757
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AT xinjianzhang newderivationandrecursivealgorithmbasedonwronskianmatrixforvandermondeinversematrix
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