Symmetric functions and the Vandermonde matrix

Oruc H., Akmaz H.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.172, sa.1, ss.49-64, 2004 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 172 Sayı: 1
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1016/j.cam.2004.01.032
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.49-64
  • Anahtar Kelimeler: Vandermonde matrix, symmetric functions, triangular and bidiagonal factorization, q-stirling numbers, Q-BERNSTEIN POLYNOMIALS, INTEGER NODES, CAUCHY, SYSTEMS
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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 x(i) = 1 + q + (...) + q(i-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. (C) 2004 Elsevier B.V. All rights reserved.