No fluctuation approximation in any desired precision for univariate function matrix representations


Demiralp M.

JOURNAL OF MATHEMATICAL CHEMISTRY, cilt.47, sa.1, ss.99-110, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Konu: 1
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1007/s10910-009-9533-5
  • Dergi Adı: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Sayfa Sayıları: ss.99-110

Özet

The operator involving problems are mostly handled by using the matrix representations of the operators over a finite set of appropriately chosen basis functions in a Hilbert space as long as the related problem permits. The algebraic operator which multiplies its operand by a function is the focus of this work. We deal with the univariate case for simplicity. We show that a rapidly converging scheme can be constructed by defining an appropriate fluctuation operator which projects, in fact, to the complement of the space spanned by appropriately chosen finite number of basis functions. What we obtain here can be used in efficient numerical integration also.