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

  • Metin Demiralp
Original Paper

Abstract

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.

Keywords

Matrix representation Fluctuation expansion Hilbert spaces Projection operators Algebraic multiplication operators 

References

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.İstanbul Teknik Üniversitesi Bilişim EnstitüsüIstanbulTurkey

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