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Journal articles on the topic 'Vandermonde determinant'

Author: Grafiati

Published: 24 April 2022

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1

Yaici, Malika, and Kamel Hariche. "A particular block Vandermonde matrix." ITM Web of Conferences 24 (2019): 01008. http://dx.doi.org/10.1051/itmconf/20192401008.

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The Vandermonde matrix is ubiquitous in mathematics and engineering. Both the Vandermonde matrix and its inverse are often encountered in control theory, in the derivation of numerical formulas, and in systems theory. In some cases block vandermonde matrices are used. Block Vandermonde matrices, considered in this paper, are constructed from a full set of solvents of a corresponding matrix polynomial. These solvents represent block poles and block zeros of a linear multivariable dynamical time-invariant system described in matrix fractions. Control techniques of such systems deal with the inverse or determinant of block vandermonde matrices. Methods to compute the inverse of a block vandermonde matrix have not been studied but the inversion of block matrices (or partitioned matrices) is very well studied. In this paper, properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. A parallelization of these algorithms is also presented. The proposed algorithms are validated by a comparison based on algorithmic complexity.

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2

Xu, Junqin, and Likuan Zhao. "An application of the Vandermonde determinant." International Journal of Mathematical Education in Science and Technology 37, no. 2 (March 15, 2006): 229–31. http://dx.doi.org/10.1080/00207390500226093.

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3

Lomidze, I. "On Some Generalizations of the Vandermonde Matrix and Their Relations with the Euler Beta-Function." gmj 1, no. 4 (August 1994): 405–17. http://dx.doi.org/10.1515/gmj.1994.405.

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Abstract A multiple Vandermonde matrix which, besides the powers of variables, also contains their derivatives is introduced and an explicit expression of its determinant is obtained. For the case of arbitrary real powers, when the variables are positive, it is proved that such generalized multiple Vandermonde matrix is positive definite for appropriate enumerations of rows and columns. As an application of these results, some relations are obtained which in the one-dimensional case give the well-known formula for the Euler beta-function.

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4

Mpimbo, Marco. "On the Convergence of Orbits in Sequence Space l^2." Tanzania Journal of Science 47, no. 3 (August 15, 2021): 1174–83. http://dx.doi.org/10.4314/tjs.v47i3.26.

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This paper discusses the convergence of orbits for diagonal operators defined on . In particular, the basis elements of are obtained using the linear combinations of the elements of the orbit. Furthermore, via the classical result of the determinant of the Vandermonde matrix, it is shown that, the more the elements of the orbit are used, the faster the convergence of the orbit to the basis elements of . Keywords: Diagonal operators; Convergence of Orbits of operators; Vandermonde matrix; Norm topology

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5

Chang, Geng-Zhe. "Planar Metric Inequalities Derived from the Vandermonde Determinant." American Mathematical Monthly 92, no. 7 (August 1985): 495. http://dx.doi.org/10.2307/2322511.

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6

Chang, Geng-Zhe. "Planar Metric Inequalities Derived from the Vandermonde Determinant." American Mathematical Monthly 92, no. 7 (August 1985): 495–99. http://dx.doi.org/10.1080/00029890.1985.11971664.

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7

Chu, Wenchang, and Xiaoyuan Wang. "Extensions of Vandermonde determinant by computing divided differences." Afrika Matematika 29, no. 1-2 (September 8, 2017): 73–79. http://dx.doi.org/10.1007/s13370-017-0527-3.

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8

Sogabe, Tomohiro, and Moawwad El-Mikkawy. "On a problem related to the Vandermonde determinant." Discrete Applied Mathematics 157, no. 13 (July 2009): 2997–99. http://dx.doi.org/10.1016/j.dam.2009.04.018.

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9

徐, 雯燕. "Application of Vandermonde Determinant in Advanced Algebra Solving." Pure Mathematics 11, no. 07 (2021): 1421–29. http://dx.doi.org/10.12677/pm.2021.117159.

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10

Ramana, D. S. "Arithmetical applications of an identity for the Vandermonde determinant." Acta Arithmetica 130, no. 4 (2007): 351–59. http://dx.doi.org/10.4064/aa130-4-4.

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11

King, R. C., F. Toumazet, and B. G. Wybourne. "The square of the Vandermonde determinant and itsq-generalization." Journal of Physics A: Mathematical and General 37, no. 3 (January 6, 2004): 735–67. http://dx.doi.org/10.1088/0305-4470/37/3/015.

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12

Meng, De-Xin, and Kuang-Zhong Li. "Darboux transformation of the second-type nonlocal derivative nonlinear Schrödinger equation." Modern Physics Letters B 33, no. 10 (April 10, 2019): 1950123. http://dx.doi.org/10.1142/s0217984919501239.

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The second-type nonlocal derivative nonlinear Schrödinger (NDNLSII) equation is studied in this paper. By constructing its [Formula: see text]-order Darboux transformations (DT) from the first-order DT, Vandermonde-type determinant solutions of the NDNLSII equation are obtained from zero seed solutions, which would be singular unless the square of eigenvalues are purely imaginary.

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13

Scharf, T., J. Thibon, and B. G. Wybourne. "Powers of the Vandermonde determinant and the quantum Hall effect." Journal of Physics A: Mathematical and General 27, no. 12 (June 21, 1994): 4211–19. http://dx.doi.org/10.1088/0305-4470/27/12/026.

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14

Ballantine, C. "Powers of the Vandermonde determinant, Schur functions and recursive formulas." Journal of Physics A: Mathematical and Theoretical 45, no. 31 (July 18, 2012): 315201. http://dx.doi.org/10.1088/1751-8113/45/31/315201.

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15

Tu, Loring W. "A partial order on partitions and the generalized Vandermonde determinant." Journal of Algebra 278, no. 1 (August 2004): 127–33. http://dx.doi.org/10.1016/j.jalgebra.2003.09.048.

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16

Respondek, Jerzy S. "Recursive Matrix Calculation Paradigm by the Example of Structured Matrix." Information 11, no. 1 (January 13, 2020): 42. http://dx.doi.org/10.3390/info11010042.

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In this paper, we derive recursive algorithms for calculating the determinant and inverse of the generalized Vandermonde matrix. The main advantage of the recursive algorithms is the fact that the computational complexity of the presented algorithm is better than calculating the determinant and the inverse by means of classical methods, developed for the general matrices. The results of this article do not require any symbolic calculations and, therefore, can be performed by a numerical algorithm implemented in a specialized (like Matlab or Mathematica) or general-purpose programming language (C, C++, Java, Pascal, Fortran, etc.).

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17

MERILÄ, VILLE. "A NONVANISHING LEMMA FOR CERTAIN PADÉ APPROXIMATIONS OF THE SECOND KIND." International Journal of Number Theory 07, no. 08 (December 2011): 1977–97. http://dx.doi.org/10.1142/s1793042111004964.

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We prove the nonvanishing lemma for explicit second kind Padé approximations to generalized hypergeometric and q-hypergeometric functions. The proof is based on an evaluation of a generalized Vandermonde determinant. Also, some immediate applications to the Diophantine approximation is given in the form of sharp linear independence measures for hypergeometric E- and G-functions in algebraic number fields with different valuations.

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18

Louck, James D. "Power of a determinant with two physical applications." International Journal of Mathematics and Mathematical Sciences 22, no. 4 (1999): 745–59. http://dx.doi.org/10.1155/s0161171299227457.

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An expression for thekth power of ann×ndeterminant inn2indeterminates(zij)is given as a sum of monomials. Two applications of this expression are given: the first is the Regge generating function for the Clebsch-Gordan coefficients of the unitary groupSU(2), noting also the relation to the 3 F2hypergeometric series; the second is to the even powers of the Vandermonde determinant, or, equivalently, all powers of the discriminant. The second result leads to an interesting map between magic square arrays and partitions and has applications to the wave functions describing the quantum Hall effect. The generalization of this map to arbitrary square arrays of nonnegative integers, having given row and column sums, is also given.

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19

Lundengård, Karl, Jonas Österberg, and Sergei Silvestrov. "Optimization of the Determinant of the Vandermonde Matrix and Related Matrices." Methodology and Computing in Applied Probability 20, no. 4 (November 14, 2017): 1417–28. http://dx.doi.org/10.1007/s11009-017-9595-y.

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20

Abu-Saris, Raghib, and Wajdi Ahmad. "Generalized Exponential Vandermonde Determinant and Hermite Multipoint Discrete Boundary Value Problem." SIAM Journal on Matrix Analysis and Applications 25, no. 4 (January 2004): 921–29. http://dx.doi.org/10.1137/s0895479803421264.

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21

Braun, Lukas. "Hilbert series of the Grassmannian and k-Narayana numbers." Communications in Mathematics 27, no. 1 (June 1, 2019): 27–41. http://dx.doi.org/10.2478/cm-2019-0003.

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AbstractWe compute the Hilbert series of the complex Grassmannian using invariant theoretic methods. This is made possible by showing that the denominator of the q-Hilbert series is a Vandermonde-like determinant. We show that the h-polynomial of the Grassmannian coincides with the k-Narayana polynomial. A simplified formula for the h-polynomial of Schubert varieties is given. Finally, we use a generalized hypergeometric Euler transform to find simplified formulae for the k-Narayana numbers, i.e. the h-polynomial of the Grassmannian.

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22

LIU, HUANING. "GOWERS UNIFORMITY NORM AND PSEUDORANDOM MEASURES OF THE PSEUDORANDOM BINARY SEQUENCES." International Journal of Number Theory 07, no. 05 (August 2011): 1279–302. http://dx.doi.org/10.1142/s1793042111004137.

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Recently there has been much progress in the study of arithmetic progressions. An important tool in these developments is the Gowers uniformity norm. In this paper we study the Gowers norm for pseudorandom binary sequences, and establish some connections between these two subjects. Some examples are given to show that the "good" pseudorandom sequences have small Gowers norm. Furthermore, we introduce two large families of pseudorandom binary sequences constructed by the multiplicative inverse and additive character, and study the pseudorandom measures and the Gowers norm of these sequences by using the estimates of exponential sums and properties of the Vandermonde determinant. Our constructions are superior to the previous ones from some points of view.

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23

SERU, FEBY. "METODE PEMBAGIAN SINTETIK UNTUK MENGHITUNG INVERS MATRIKS VANDERMONDE DAN APLIKASINYA DALAM MEMPREDIKSI HARGA SAHAM." Jurnal Matematika UNAND 10, no. 4 (October 21, 2021): 519. http://dx.doi.org/10.25077/jmu.10.4.519-526.2021.

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Vandermonde memiliki peranan yang penting dalam bidang matematika dan terapannya. Terdapat beberapa metode untuk menghitung invers matriks Vandermode, diantaranya metode pembagian sintetik. Metode ini memiliki kelebihan yaitu tidak memerlukan perkalian matriks maupun perhitungan determinan dalam menghitung invers matriks. Tujuan dari penelitian ini adalah mengaplikasikan metode tersebut untuk memprediksi harga saham BBRI pada bulan April dan Agustus tahun 2019. Hasil yang diperoleh adalah harga saham pada bulan April sebesar IDR 4.330 dan sebesar IDR 5.180 pada bulan Agustus.Kata Kunci: Matriks Vandermonde, Pembagian Sintetik, Prediksi

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24

Wang, Lei, Yi-Tian Gao, and Xiao-Ling Gai. "Odd-Soliton-Like Solutions for the Variable-Coefficient Variant Boussinesq Model in the Long Gravity Waves." Zeitschrift für Naturforschung A 65, no. 10 (October 1, 2010): 818–28. http://dx.doi.org/10.1515/zna-2010-1008.

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Under investigation in this paper, with symbolic computation, is a variable-coefficient variant Boussinesq (vcvB) model for the nonlinear and dispersive long gravity waves travelling in two horizontal directions with varying depth. Connection between the vcvB model and a variable-coefficient Broer-Kaup (vcBK) system is revealed under certain constraints. By means of the N-fold Darboux transformation for the vcBK system, odd-soliton-like solutions in terms of the Vandermonde-like determinant for the vcvB model are derived. Dynamics of those solutions is analyzed graphically, on the three-parallel solitonic waves, head-on collisions, double structures, and inelastic interactions. It is reported that the shapes of the soliton-like waves and separation distance between them depend on the spectrum parameters and the variable coefficients affect the velocities of the waves. Our results could be helpful in interpreting certain nonlinear wave phenomena in fluid dynamics.

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25

Granata, Antonio. "Asymptotic Behaviors of Wronskians and Finite Asymptotic Expansions in the Real Domain - Part I: Scales of Regularly- or Rapidly-Varying Functions." International Journal of Advanced Research in Mathematics 9 (June 2017): 1–33. http://dx.doi.org/10.18052/www.scipress.com/ijarm.9.1.

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In a previous series of papers we established a general theory of finite asymptotic expansions in the real domain for functions f of one real variable sufficiently-regular on a deleted neighborhood of a point x0 ∈ R, a theory based on the use of a uniquely-determined linear differential operator L associated to the given asymptotic scale and wherein various sets of asymptotic expansions are characterized by the convergence of improper integrals involving both the operator L applied to f and certain weight functions constructed by means of Wronskians of the given scale. Very special cases apart, Wronskians have quite complicated expressions and unrecognizable asymptotic behaviors; however in the present work, split in two parts, we highlight some approaches for determining the exact asymptotic behavior of a Wronskian when the involved functions are regularly- or rapidly-varying functions of higher order. This first part contains: (i) some preliminary results on the asymptotic behavior of a determinant whose entries are asymptotically equivalent to the entries of a Vandermonde determinant; (ii) the fundamental results about the asymptotic behaviors of Wronskians involving scales of functions all of which are either regularly (or, more generally, smoothly) varying or rapidly varying of a suitable higher order. A lot of examples and applications to the theory of asymptotic expansions in the real domain are given.

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26

Varchenko, A. N. "THE EULER BETA-FUNCTION, THE VANDERMONDE DETERMINANT, LEGENDRE'S EQUATION, AND CRITICAL VALUES OF LINEAR FUNCTIONS ON A CONFIGURATION OF HYPERPLANES. I." Mathematics of the USSR-Izvestiya 35, no. 3 (June 30, 1990): 543–71. http://dx.doi.org/10.1070/im1990v035n03abeh000717.

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27

Varchenko, A. N. "THE EULER BETA-FUNCTION, THE VANDERMONDE DETERMINANT, LEGENDRE'S EQUATION, AND CRITICAL VALUES OF LINEAR FUNCTIONS ON A CONFIGURATION OF HYPERPLANES. II." Mathematics of the USSR-Izvestiya 36, no. 1 (February 28, 1991): 155–67. http://dx.doi.org/10.1070/im1991v036n01abeh001960.

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28

Schlickewei, Hans, and Carlo Viola. "Generalized Vandermonde determinants." Acta Arithmetica 95, no. 2 (2000): 123–37. http://dx.doi.org/10.4064/aa-95-2-123-137.

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29

Watanabe, Junzo, and Kohji Yanagawa. "Vandermonde determinantal ideals." MATHEMATICA SCANDINAVICA 125, no. 2 (October 19, 2019): 179–84. http://dx.doi.org/10.7146/math.scand.a-114906.

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We show that the ideal generated by maximal minors (i.e., $k+1$-minors) of a $(k+1) \times n$ Vandermonde matrix is radical and Cohen-Macaulay. Note that this ideal is generated by all Specht polynomials with shape $(n-k,1, …,1)$.

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30

Yang, Shang-jun, Hua-zhang Wu, and Quan-bing Zhang. "Generalization of Vandermonde determinants." Linear Algebra and its Applications 336, no. 1-3 (October 2001): 201–4. http://dx.doi.org/10.1016/s0024-3795(01)00319-6.

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31

KURNIA SARI, DILLA. "PEMBUKTIAN RUMUS BENTUK TUTUP BEDA PUSAT BERDASARKAN DERET TAYLOR." Jurnal Matematika UNAND 6, no. 3 (November 3, 2017): 55. http://dx.doi.org/10.25077/jmu.6.3.55-62.2017.

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Pada makalah ini dibahas pembuktian dari rumus bentuk tutup beda pusat berdasarkan deret Taylor untuk menghampiri turunan pertama dari suatu fungsi. Pembuktian rumus bentuk tutup tersebut menggunakan sifat-sifat determinan matriks Vandermonde dan beberapa manipulasi aljabar. Kata Kunci: Rumus beda pusat, deret Taylor, matriks Vandermonde

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32

Bahturin, Yuri, Amitai Regev, and Doron Zeilberger. "Commutation relations and Vandermonde determinants." European Journal of Combinatorics 30, no. 5 (July 2009): 1271–76. http://dx.doi.org/10.1016/j.ejc.2008.09.024.

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33

Muhlbach, G. "Computation of Cauchy-Vandermonde Determinants." Journal of Number Theory 43, no. 1 (January 1993): 74–81. http://dx.doi.org/10.1006/jnth.1993.1008.

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34

Spież, Stanisław, Jerzy Urbanowicz, and Paul van Wamelen. "Divisibility properties of generalized Vandermonde determinants." Acta Arithmetica 110, no. 4 (2003): 361–79. http://dx.doi.org/10.4064/aa110-4-4.

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35

Li, Lei, and Tadao Nakamura. "Fast parallel algorithms for vandermonde determinants." International Journal of Computer Mathematics 73, no. 4 (January 2000): 479–86. http://dx.doi.org/10.1080/00207160008804911.

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36

Flowe, Randolph P., and Gary A. Harris. "A Note on Generalized Vandermonde Determinants." SIAM Journal on Matrix Analysis and Applications 14, no. 4 (October 1993): 1146–51. http://dx.doi.org/10.1137/0614079.

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37

Zhang, Zhi-Hua, Yu-Dong Wu, and H. M. Srivastava. "Generalized Vandermonde determinants and mean values." Applied Mathematics and Computation 202, no. 1 (August 2008): 300–310. http://dx.doi.org/10.1016/j.amc.2008.02.016.

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38

Lita da Silva, João. "On One Type of Generalized Vandermonde Determinants." American Mathematical Monthly 125, no. 5 (April 12, 2018): 433–42. http://dx.doi.org/10.1080/00029890.2018.1427393.

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39

D’Andrea, Carlos, and Luis Felipe Tabera. "Tropicalization and irreducibility of generalized Vandermonde determinants." Proceedings of the American Mathematical Society 137, no. 11 (November 1, 2009): 3647. http://dx.doi.org/10.1090/s0002-9939-09-09951-1.

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40

Gasca, Mariano, and José J. Martínez. "Bivariate Hermite-Birkhoff interpolation and Vandermonde determinants." Numerical Algorithms 3, no. 1 (December 1992): 193–99. http://dx.doi.org/10.1007/bf02141928.

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41

Martin, K., and J. M. De Olazabal. "An extension of Vandermonde's determinant." International Journal of Mathematical Education in Science and Technology 25, no. 5 (September 1994): 665–67. http://dx.doi.org/10.1080/0020739940250506.

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42

Putri, Ade, and Radhiatul Husna. "PEMBUKTIAN BENTUK TUTUP RUMUS BEDA MAJU BERDASARKAN DERET TAYLOR." Jurnal Matematika UNAND 5, no. 4 (November 28, 2016): 1. http://dx.doi.org/10.25077/jmu.5.4.1-8.2016.

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Abstrak. Pada artikel ini dibahas pembuktian bentuk tutup rumus beda majuberdasarkan deret Taylor untuk menghampiri secara numerik turunan pertama darifungsi satu variabel. Pembuktian bentuk tutup tersebut menggunakan sifat-sifat determinanmatriks Vandermonde dan beberapa manipulasi aljabar.Kata Kunci: Rumus beda maju, deret Taylor, turunan numerik, determinan matriksVandermonde

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43

De Marchi, Stefano, and Konstantin Usevich. "On certain multivariate Vandermonde determinants whose variables separate." Linear Algebra and its Applications 449 (May 2014): 17–27. http://dx.doi.org/10.1016/j.laa.2014.01.034.

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44

Barbero, Stefano. "Generalized Vandermonde determinants and characterization of divisibility sequences." Journal of Number Theory 173 (April 2017): 371–77. http://dx.doi.org/10.1016/j.jnt.2016.09.025.

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45

Aliev, M. S., and G. Y. Bru Mantch. "The Vandermonde determinants with two powers crossed out." Herald of Dagestan State University 32, no. 3 (2017): 67–73. http://dx.doi.org/10.21779/2542-0321-2017-32-3-67-73.

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46

Benjamin, Arthur T., and Gregory P. Dresden. "A Combinatorial Proof of Vandermonde's Determinant." American Mathematical Monthly 114, no. 4 (April 2007): 338–41. http://dx.doi.org/10.1080/00029890.2007.11920421.

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47

Steudel, H., R. Meinel, and G. Neugebauer. "Vandermonde-like determinants and N-fold Darboux/Bäcklund transformations." Journal of Mathematical Physics 38, no. 9 (September 1997): 4692–95. http://dx.doi.org/10.1063/1.532115.

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48

Cervellino, A., and S. Ciccariello. "The determinants of some multilevel Vandermonde and Toeplitz matrices." Journal of Physics A: Mathematical and General 38, no. 45 (October 26, 2005): 9731–39. http://dx.doi.org/10.1088/0305-4470/38/45/001.

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49

Quinn, Jennifer J. "Visualizing Vandermonde's determinant through nonintersecting lattice paths." Journal of Statistical Planning and Inference 140, no. 8 (August 2010): 2346–50. http://dx.doi.org/10.1016/j.jspi.2010.01.029.

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50

Donno, Giuseppe De. "Generalized Vandermonde determinants for reversing Taylor's formula and application to hypoellipticity." Tamkang Journal of Mathematics 38, no. 2 (June 30, 2007): 183–89. http://dx.doi.org/10.5556/j.tkjm.38.2007.89.

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The problem of the hypoellipticity of the linear partial differential operators with constant coefficients was completely solved by H"{o}r-man-der in [5]. He listed many equivalent algebraic conditions on the polynomial symbol of the operator, each necessary and sufficient for hypoellipticity. In this paper we employ two Mitchell's Theorems (1881) regarding a type of Generalized Vandermonde Determinants, for inverting Taylor's formula of polynomials in several variables with complex coefficients. We obtain then a more direct and easy proof of an equivalence for the mentioned H"{o}r-man-der's hypoellipticity conditions.

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