Oruç, Halil LU factorization of the Vandermonde matrix and its applications. (English) Zbl 1152.15303 Appl. Math. Lett. 20, No. 9, 982-987 (2007). 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. Cited in 8 Documents MSC: 15A23 Factorization of matrices 39A13 Difference equations, scaling (\(q\)-differences) Keywords:Vandermonde matrix; symmetric functions; triangular and bidiagonal factorization; \(q\)-pascal matrix; \(q\)-difference equation Software:mctoolbox PDF BibTeX XML Cite \textit{H. Oruç}, Appl. Math. Lett. 20, No. 9, 982--987 (2007; Zbl 1152.15303) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.