05256992

j

05256992 Liang, Yan Lai Yang, Zheng Hong A fast algorithm for inversion of confluent polynomial Vandermonde matrices with a general recurrence structure. Int. J. Pure Appl. Math. 41, No. 2, 183-194 (2007). 2007 Academic Publications, Sofia EN Vandermonde matrix matrix inversion general polynomial basis Chebyshev polynomial basis algorithm numerical experiment Gauss elimination A Vandermonde type matrix is encountered in many theoretical disciplines supporting mathematics itself (interpolation and optimization problems, numerical integration, etc.) and physical areas related with initial value problems of ordinary differential system. In practice various algebraic operation with Vandermonde matrices are necessary to be done either analytically or numerically. The paper represents an excellent contribution providing a new algorithm for inversion of a special type of the Vandermonde matrix. After a history of the problem the authors present some basic definitions including their proofs. Recurrence formulae for the inverse matrix enumeration are presented. The algorithm itself is introduced in a form of five finite partial numerical processes. Each of them is clearly stated and described in the first step and summarized in an outline of a computer code. In the last part a numerical experiment is presented. For demonstration the first type Chebyshev polynomial as basis is selected. Results obtained using the proposed algorithm and the Gauss elimination are compared by means of the Frobenius norm of the residuals. A table of results makes evident the advantages of the proposed algorithm for several degrees of polynomial basis. It should be remarked that some self-contained nomenclature and other amendments would be useful. The explanation brevity is sometimes to the detriment of the comprehensibility. Jiri N\'aprstek (Praha)