QUADRATUREFORMULASFORTHE FOURIER-CHEBYSHEVCOEFFICIENTS
QUADRATURE FORMULAS FOR THE FOURIER-CHEBYSHEV COEFFICIENTS
Апстракт
We consider the well known Micchelli-Rivlin quadrature formula, of
highest algebraic degree of precision, for the Fourier-Chebyshev coefficients.
For analytic functions the remainder term of this quadrature formula can
be represented as a contour integral with a complex kernel. We study the
kernel, on elliptic contours with foci at the points ∓1 and a sum of semiaxes ρ > 1, for the quoted quadrature formula. Starting from the explicit
expression of the kernel, we determine the locations on the ellipses where
maximum modulus of the kernel is attained. So we derive effective L
∞-
error bounds for this quadrature formula. Complex-variable methods are
used to obtain expansions of the error in the Micchelli-Rivlin quadrature
formula over the interval [−1, 1]. Finally, effective L
1
-error bounds are also
derived for this quadrature formula
Извор:
4th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA, BOOK OF ABSTRACTS, Trebinje, 06-07 June 2014, 2014, 57-57Издавач:
- University of East Sarajevo Mathematical, Society of the Republic of Srpska
Институција/група
Mašinski fakultetTY - CONF AU - Pejcev, Aleksandar AU - Spalević, Miodrag PY - 2014 UR - https://machinery.mas.bg.ac.rs/handle/123456789/5135 AB - We consider the well known Micchelli-Rivlin quadrature formula, of highest algebraic degree of precision, for the Fourier-Chebyshev coefficients. For analytic functions the remainder term of this quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points ∓1 and a sum of semiaxes ρ > 1, for the quoted quadrature formula. Starting from the explicit expression of the kernel, we determine the locations on the ellipses where maximum modulus of the kernel is attained. So we derive effective L ∞- error bounds for this quadrature formula. Complex-variable methods are used to obtain expansions of the error in the Micchelli-Rivlin quadrature formula over the interval [−1, 1]. Finally, effective L 1 -error bounds are also derived for this quadrature formula PB - University of East Sarajevo Mathematical, Society of the Republic of Srpska C3 - 4th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA, BOOK OF ABSTRACTS, Trebinje, 06-07 June 2014 T1 - QUADRATUREFORMULASFORTHE FOURIER-CHEBYSHEVCOEFFICIENTS T1 - QUADRATURE FORMULAS FOR THE FOURIER-CHEBYSHEV COEFFICIENTS EP - 57 SP - 57 UR - https://hdl.handle.net/21.15107/rcub_machinery_5135 ER -
@conference{ author = "Pejcev, Aleksandar and Spalević, Miodrag", year = "2014", abstract = "We consider the well known Micchelli-Rivlin quadrature formula, of highest algebraic degree of precision, for the Fourier-Chebyshev coefficients. For analytic functions the remainder term of this quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points ∓1 and a sum of semiaxes ρ > 1, for the quoted quadrature formula. Starting from the explicit expression of the kernel, we determine the locations on the ellipses where maximum modulus of the kernel is attained. So we derive effective L ∞- error bounds for this quadrature formula. Complex-variable methods are used to obtain expansions of the error in the Micchelli-Rivlin quadrature formula over the interval [−1, 1]. Finally, effective L 1 -error bounds are also derived for this quadrature formula", publisher = "University of East Sarajevo Mathematical, Society of the Republic of Srpska", journal = "4th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA, BOOK OF ABSTRACTS, Trebinje, 06-07 June 2014", title = "QUADRATUREFORMULASFORTHE FOURIER-CHEBYSHEVCOEFFICIENTS, QUADRATURE FORMULAS FOR THE FOURIER-CHEBYSHEV COEFFICIENTS", pages = "57-57", url = "https://hdl.handle.net/21.15107/rcub_machinery_5135" }
Pejcev, A.,& Spalević, M.. (2014). QUADRATUREFORMULASFORTHE FOURIER-CHEBYSHEVCOEFFICIENTS. in 4th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA, BOOK OF ABSTRACTS, Trebinje, 06-07 June 2014 University of East Sarajevo Mathematical, Society of the Republic of Srpska., 57-57. https://hdl.handle.net/21.15107/rcub_machinery_5135
Pejcev A, Spalević M. QUADRATUREFORMULASFORTHE FOURIER-CHEBYSHEVCOEFFICIENTS. in 4th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA, BOOK OF ABSTRACTS, Trebinje, 06-07 June 2014. 2014;:57-57. https://hdl.handle.net/21.15107/rcub_machinery_5135 .
Pejcev, Aleksandar, Spalević, Miodrag, "QUADRATUREFORMULASFORTHE FOURIER-CHEBYSHEVCOEFFICIENTS" in 4th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA, BOOK OF ABSTRACTS, Trebinje, 06-07 June 2014 (2014):57-57, https://hdl.handle.net/21.15107/rcub_machinery_5135 .