论文信息 - Comments on "Inversion of the VanderMonde matrix"

Comments on "Inversion of the VanderMonde matrix"

The authors comment that Neagoe (see ibid., vol.3, no.4, p.119-120, 1996) derives, in a direct manner, an explicit formula for the inverse of the VanderMonde matrix. They point out that an alternative derivation of this formula, based on the Lagrange interpolation formula, is given in Macon and Spitzbart (1958). Their formula appears to be slightly different, primarily because of the manner in which the sign of each term is determined, but is nevertheless equivalent to the one presented by Neagoe.

Russell J. Niederjohn | James A. Heinen | J. Heinen | R. Niederjohn

[1] İzzet Cem Göknar. Obtaining the inverse of the generalized Vandermonde matrix of the most general type , 1973 .

[2] An inversion procedure of the generalized Vandermonde matrix , 1971 .

[3] H. Wertz,et al. On the numerical inversion of a recurrent problem: The Vandermonde matrix , 1965 .

[4] A. Spitzbart,et al. Inverses of Vandermonde Matrices , 1958 .

[5] L. Lupas. On the computation of the generalized Vandermonde matrix inverse , 1975 .

[6] A. C. Aitken. Determinants and matrices , 1940 .

[7] J. Tou,et al. On the reverse Vandermonde matrix , 1966 .

[8] I. Kaufman,et al. The inversion of the Vandermonde matrix and transformation to the Jordan canonical form , 1969 .

[9] The inverse of the generalized vandermonde matrix through the partial fraction expansion , 1974 .

[10] Richard W. Hamming,et al. Numerical Methods for Scientists and Engineers , 1963 .

[11] F. Csaki,et al. Some notes on the inversion of confluent Vandermonde matrices , 1975 .

[12] G. Reis. A matrix formulation for the inverse Vandermonde matrix , 1967, IEEE Transactions on Automatic Control.

[13] Walter Gautschi,et al. On inverses of Vandermonde and confluent Vandermonde matrices. II , 1963 .

[14] T. Muir. The Theory of Determinants in the Historical Order of Development , 1920 .

[15] R. Schappelle. The inverse of the confluent Vandermonde matrix , 1972 .

[16] J. Tou,et al. Determination of the inverse Vandermonde matrix , 1964 .