Enumerative combinatorics
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Fast algorithms of Bjo¨rck-Pereyra type for solving Cauchy-Vandermonde linear systems
Applied Numerical Mathematics
Regular Article: Generalized Binomial Coefficients and the Subset驴Subspace Problem
Advances in Applied Mathematics
On the convergence and iterates of q-Bernstein polynomials
Journal of Approximation Theory
q-Bernstein polynomials and Bézier curves
Journal of Computational and Applied Mathematics
Economical error estimates for block implicit methods for ODEs via deferred correction
Applied Numerical Mathematics
Structured matrices in the application of bivariate interpolation to curve implicitization
Mathematics and Computers in Simulation
Note: On a problem related to the Vandermonde determinant
Discrete Applied Mathematics
Economical error estimates for block implicit methods for ODEs via deferred correction
Applied Numerical Mathematics
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This work deduces the lower and the upper triangular factors of the inverse of the Vandermonde matrix using symmetric functions and combinatorial identities. The L and U matrices are in turn factored as bidiagonal matrices. The elements of the upper triangular matrices in both the Vandermonde matrix and its inverse are obtained recursively. The particular value xi=1 + q +...+ qi-1 in the indeterminates of the Vandermonde matrix is investigated and it leads to q-binomial and q-Stirling matrices. It is also shown that q-Stirling matrices may be obtained from the Pascal matrix.