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LU factorization of the Vandermonde matrix and its applications. (English) Zbl 1152.15303
Summary: A scaled version of the lower and the upper triangular factors of the inverse of the Vandermonde matrix is given. Two applications of the $$q$$-Pascal matrix resulting from the factorization of the Vandermonde matrix at the $$q$$-integer nodes are introduced.

##### MSC:
 15A23 Factorization of matrices 39A13 Difference equations, scaling ($$q$$-differences)
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##### References:
 [1] Aceto, L.; Trigante, D., The matrices of Pascal and other greats, Amer. math. monthly, 108, 232-244, (2001) · Zbl 1002.15024 [2] Andrews, G.E., The theory of partitions, (1998), Cambridge University Press Cambridge · Zbl 0906.05004 [3] Andrews, G.E.; Askey, R.; Roy, R., Special functions, () [4] Farin, G., Curves and surfaces for CAGD, A practical guide, (2002), Academic Press San Diego [5] Gohberg, I.; Koltracht, I., Triangular factors of Cauchy and Vandermonde matrices, Integral equations operator theory, 26, 46-59, (1996) · Zbl 0858.15006 [6] Higham, N.J., Accuracy and stability of numerical algorithms, (2002), SIAM Philadelphia · Zbl 1011.65010 [7] Martínez, J.J.; Peña, J.M., Factorization of cauchy – vandermonde matrices, Linear algebra appl., 284, 229-237, (1998) · Zbl 0935.65017 [8] Oruç, H.; Phillips, G.M., Explicit factorization of the Vandermonde matrix, Linear algebra appl., 315, 113-123, (2000) · Zbl 0959.15011 [9] Oruç, H.; Akmaz, H.K., Symmetric functions and the Vandermonde matrix, J. comput. appl. math., 172, 49-64, (2004) · Zbl 1063.15023 [10] Oruç, H.; Phillips, G.M., $$q$$-Bernstein polynomials and Bézier curves, J. comput. appl. math., 151, 1-12, (2003) · Zbl 1014.65015 [11] Phillips, G.M., Interpolation and approximation by polynomials, (2003), Springer-Verlag New York · Zbl 1023.41002 [12] Yang, S.L., On the $$L U$$ factorization of the Vandermonde matrix, Discrete appl. math., 146, 102-105, (2005) · Zbl 1065.15014
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