A Note on Generalized Vandermonde Determinants

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Previous article Next article A Note on Generalized Vandermonde DeterminantsRandolph P. Flowe and Gary A. HarrisRandolph P. Flowe and Gary A. Harrishttps://doi.org/10.1137/0614079PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThis note contains elementary derivations of explicit formulae for the determinants of two types of matrices which are generalized versions of that which is commonly known as the Vandermonde matrix.[1] R. P. Grimaldi, Discrete and Combinatorial Mathematics, Addison-Wesley, Reading, MA, 1989 0679.05001 Google Scholar[2] Steven L. Kleiman, Problem 15: rigorous foundation of Schubert's enumerative calculusMathematical developments arising from Hilbert problems (Proc. Sympos. Pure Math., Northern Illinois Univ., De Kalb, Ill., 1974), Amer. Math. Soc., Providence, R. I., 1976, 445–482. Proc. Sympos. Pure Math., Vol. XXVIII 55:2946 0336.14001 CrossrefGoogle Scholar[3] C. Martin, , J. Miller and , K. Pearce, Sums of exponentials with polynomial coefficients, Appl. Math. Comput., 40 (1990), 33–39 10.1016/0096-3003(90)90096-L 91g:65019 0713.65002 CrossrefISIGoogle Scholar[4] J. Stoer and , R. Bulirsch, Introduction to numerical analysis, Springer-Verlag, New York, 1980ix+609, R. Bartels, W. Gautschi, and C. Witzgall, translators 83d:65002 0423.65002 CrossrefGoogle ScholarKeywordsgeneralized Vandermonde matricesHermite interpolationlinear recursion relationdegree of a Grassmann manifold Previous article Next article FiguresRelatedReferencesCited ByDetails Common values of a class of linear recurrencesIndagationes Mathematicae, Vol. 33, No. 6 | 1 Nov 2022 Cross Ref Universal Skolem Sets2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) | 29 Jun 2021 Cross Ref Asymptotic Waveform Evaluation With Higher Order PolesIEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 68, No. 4 | 1 Apr 2021 Cross Ref On the Distance Between Two Algebraic NumbersBulletin of the Malaysian Mathematical Sciences Society, Vol. 43, No. 4 | 6 November 2019 Cross Ref Hermite–Thue equation: Padé approximations and Siegel's lemmaJournal of Number Theory, Vol. 191 | 1 Oct 2018 Cross Ref On One Type of Generalized Vandermonde DeterminantsThe American Mathematical Monthly, Vol. 125, No. 5 | 12 April 2018 Cross Ref Generalized Vandermonde determinants and characterization of divisibility sequencesJournal of Number Theory, Vol. 173 | 1 Apr 2017 Cross Ref Correlatively Precoded OFDM With Reduced PAPRIEEE Transactions on Vehicular Technology, Vol. 65, No. 3 | 1 Mar 2016 Cross Ref Spectrally Efficient OFDM Pilot Waveform for Channel EstimationIEEE Transactions on Communications | 1 Jan 2016 Cross Ref On a Recursion Formula Related to Confluent VandermondeThe American Mathematical Monthly, Vol. 122, No. 8 | 1 Jan 2015 Cross Ref A Noncommutative Algebraic Operational Calculus for Boundary ProblemsMathematics in Computer Science, Vol. 7, No. 2 | 31 May 2013 Cross Ref Fine Spectra of Symmetric Toeplitz OperatorsAbstract and Applied Analysis, Vol. 2012 | 1 Jan 2012 Cross Ref A new transform for solving the noisy complex exponentials approximation problemJournal of Approximation Theory, Vol. 155, No. 1 | 1 Nov 2008 Cross Ref Extremal Problems of Information CombiningIEEE Transactions on Information Theory, Vol. 54, No. 1 | 1 Jan 2008 Cross Ref Closed form summation of 𝐶-finite sequencesTransactions of the American Mathematical Society, Vol. 359, No. 3 | 12 September 2006 Cross Ref The factorization of block matrices with generalized geometric progression rowsLinear Algebra and its Applications, Vol. 387 | 1 Aug 2004 Cross Ref Generalized Exponential Vandermonde Determinant and Hermite Multipoint Discrete Boundary Value ProblemRaghib Abu-Saris and Wajdi AhmadSIAM Journal on Matrix Analysis and Applications, Vol. 25, No. 4 | 31 July 2006AbstractPDF (140 KB)Polynomials arising in factoring generalized Vandermonde determinants: an algorithm for computing their coefficientsMathematical and Computer Modelling, Vol. 34, No. 3-4 | 1 Aug 2001 Cross Ref The Power-Compositions Determinant and Its Application to Global OptimizationJosep M. Brunat and Antonio MontesSIAM Journal on Matrix Analysis and Applications, Vol. 23, No. 2 | 31 July 2006AbstractPDF (157 KB)Advanced Determinant CalculusThe Andrews Festschrift | 1 Jan 2001 Cross Ref Volume 14, Issue 4| 1993SIAM Journal on Matrix Analysis and Applications History Submitted:10 June 1991Accepted:16 February 1992Published online:31 July 2006 InformationCopyright © 1993 © Society for Industrial and Applied MathematicsKeywordsgeneralized Vandermonde matricesHermite interpolationlinear recursion relationdegree of a Grassmann manifoldMSC codes15A1541A0 65F4065Q05PDF Download Article & Publication DataArticle DOI:10.1137/0614079Article page range:pp. 1146-1151ISSN (print):0895-4798ISSN (online):1095-7162Publisher:Society for Industrial and Applied Mathematics