Symmetric functions and the Vandermonde matrix

DOI10.1016/j.cam.2004.01.032zbMath1063.15023OpenAlexW2156010507MaRDI QIDQ1883472

Hakan K. Akmaz, Halil Oruç

Publication date: 12 October 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2004.01.032

zbMATH Keywords

inverse matrixsymmetric functionsStirling matrixVandermonde matrixPascal matrixtriangular factorizationbidiagonal factorizationLDU factorizationcombinatorial numbersq-Stirling numbers

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Theory of matrix inversion and generalized inverses (15A09) Symmetric functions and generalizations (05E05) Other combinatorial number theory (11B75) Hermitian, skew-Hermitian, and related matrices (15B57) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (11)

Unnamed Item ⋮ Parallel and \(k\)-out-of-\(n\): \(G\) systems with nonidentical components and their mean residual life functions ⋮ Using q-calculus to study LDLt factorization of a certain Vandermonde matrix ⋮ Structured matrices in the application of bivariate interpolation to curve implicitization ⋮ On two kinds of \(q\)-analogues of generalized Stirling numbers ⋮ On a problem related to the Vandermonde determinant ⋮ Economical error estimates for block implicit methods for ODEs via deferred correction. ⋮ A generalization of rational Bernstein-Bézier curves ⋮ LU factorization of the Vandermonde matrix and its applications ⋮ Tensor product \(q\)-Bernstein polynomials ⋮ Hyperderivative power sums, Vandermonde matrices, and Carlitz multiplication coefficients

Cites Work

• Factorizations of Cauchy-Vandermonde matrices
• Vandermonde matrices on integer nodes
• A trinomial analogue of Bailey's lemma and \(N=2\) superconformal invariance
• Generalized binomial coefficients and the subset-subspace problem
• The fast generalized Parker-Traub algorithm for inversion of Vandermonde and related matrices
• Fast algorithms of Björck-Pereyra type for solving Cauchy-Vandermonde linear systems
• Explicit factorization of the Vandermonde matrix
• Two millennia of mathematics. From Archimedes to Gauss
• Interpolation and approximation by polynomials
• \(q\)-Bernstein polynomials and Bézier curves
• On the convergence and iterates of \(q\)-Bernstein polynomials
• Triangular factors of Cauchy and Vandermonde matrices
• The q-Stirling numbers of first and second kinds
• Convexity and generalized Bernstein polynomials
• Solution of Vandermonde systems of equations
• Vandermonde matrices on integer nodes: The rectangular case
• Stirling matrix via Pascal matrix
• The linear algebra of the generalized Pascal matrix
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