Zobrazeno 1 - 10
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pro vyhledávání: '"Sotirios E. Notaris"'
Autor:
Sotirios E. Notaris
Publikováno v:
Numerische Mathematik. 142:129-147
Consider a (nonnegative) measure $$d\sigma $$ with support in the interval [a, b] such that the respective orthogonal polynomials satisfy a three-term recurrence relation with coefficients $$\alpha _{n}=\left\{ \begin{array}{ll} \alpha _{e},&{}n~{\hb
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a50838fc15557f52c3b997e02d9b16cf
https://doi.org/10.1007/s00211-018-1009-8
https://doi.org/10.1007/s00211-018-1009-8
Autor:
Sotirios E. Notaris
Publikováno v:
BIT Numerical Mathematics. 58:179-198
It is well known that the Gauss–Kronrod quadrature formula does not always exist with real and distinct nodes and positive weights. In 1996, in an attempt to find an alternative to the Gauss–Kronrod formula for estimating the error of the Gauss q
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1e9ef5cfbd3d3e9dbe00cf8cfb6dd4fa
https://doi.org/10.1007/s10543-017-0672-y
https://doi.org/10.1007/s10543-017-0672-y
Autor:
Sotirios E. Notaris
Publikováno v:
BIT Numerical Mathematics. 56:705-728
We consider interpolatory quadrature formulae relative to the Legendre weight function $$w(t)=1$$ on the interval $$[-1,1]$$ . On certain spaces of analytic functions the error term of these formulae is a continuous linear functional. We obtain new e
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7a3388c37572b54bd52c10e877e37948
https://doi.org/10.1007/s10543-015-0569-6
https://doi.org/10.1007/s10543-015-0569-6
Autor:
Sotirios E. Notaris
Publikováno v:
Numerische Mathematik. 133:279-302
We consider an interpolatory quadrature formula having as nodes the zeros of the nth degree Chebyshev polynomial of the second kind, on which the Fejer formula of the second kind is based, and the additional points $$\pm \tau _{c}=\pm \cos \frac{\pi
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https://doi.org/10.1007/s00211-015-0750-5
https://doi.org/10.1007/s00211-015-0750-5
Autor:
Sotirios E. Notaris
Publikováno v:
Mathematics of Computation. 84:2843-2865
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ecac47a3d6330ad9b095eceafb4213fa
https://doi.org/10.1090/mcom/2944
https://doi.org/10.1090/mcom/2944
Autor:
Sotirios E. Notaris
Publikováno v:
Journal of Computational and Applied Mathematics. 257:180-194
We study two product integration rules, one for the Chebyshev weight of the first-kind based on the Chebyshev abscissae of the second-kind, and another one constructed the other way around, i.e., relative to the Chebyshev weight of the second-kind an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::17a38b7f8bb23069fed71015f7792d32
https://doi.org/10.1016/j.cam.2013.08.013
https://doi.org/10.1016/j.cam.2013.08.013
Autor:
Sotirios E. Notaris
Publikováno v:
BIT Numerical Mathematics. 50:123-147
In certain spaces of analytic functions the error term of the Gauss-Radau quadrature formula relative to a (nonnegative) weight function is a continuous linear functional. We compute or estimate the norm of the error functional for any one of the fou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::175a7d5e246bfba45121d01fffe67014
https://doi.org/10.1007/s10543-010-0252-x
https://doi.org/10.1007/s10543-010-0252-x
Autor:
Sotirios E. Notaris
Publikováno v:
Numerical Algorithms. 49:315-329
We consider interpolatory quadrature formulae, relative to the Legendre weight function w(t) = 1 on [ − 1,1], having as nodes the zeros of any one of the nth degree orthogonal polynomials relative to the Bernstein–Szego weight functions $$w_{\gam
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fa51c9c93baa24986d344e0811a914f4
https://doi.org/10.1007/s11075-008-9176-9
https://doi.org/10.1007/s11075-008-9176-9
Autor:
Sotirios E. Notaris
Publikováno v:
Mathematics of Computation. 75:1217-1232
We evaluate explicitly the integrals ∫ 1 -1 π n (t)/(r t)dt, |r| ≠ 1, with the π n being any one of the four Chebyshev polynomials of degree n. These integrals are subsequently used in order to obtain error bounds for interpolatory quadrature f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::459b2561015c387d7b45429cd89ad166
https://doi.org/10.1090/s0025-5718-06-01859-x
https://doi.org/10.1090/s0025-5718-06-01859-x
Autor:
Sotirios E. Notaris
Publikováno v:
Numerische Mathematik. 103:99-127
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::174ef1aa9fe07978d6cf873723efbe49
https://doi.org/10.1007/s00211-005-0670-x
https://doi.org/10.1007/s00211-005-0670-x