Computation of Generalized Averaged Gaussian Quadrature Rules
Apstrakt
The estimation of the quadrature error of a Gauss quadrature rule when applied to the
approximation of an integral determined by a real-valued integrand and a real-valued
nonnegative measure with support on the real axis is an important problem in scientific
computing. Laurie [2] developed anti-Gauss quadrature rules as an aid to estimate this error.
Under suitable conditions the Gauss and associated anti-Gauss rules give upper and lower
bounds for the value of the desired integral. It is then natural to use the average of
Gauss and anti-Gauss rules as an improved approximation of the integral. Laurie also
introduced these averaged rules. More recently, the author derived new averaged Gauss
quadrature rules that have higher degree of exactness for the same number of nodes as the
averaged rules proposed by Laurie. In [2], [5], [3] stable numerical procedures for
computation of the corresponding averaged Gaussian rules are proposed. An analogous
procedure can be applied also f...or a more general class of weighted averaged Gaussian rules
introduced in [1]. Those results are presented in [4]. Here we we give a survey of the quoted
results, which are obtained jointly with L. Reichel (Kent State Univ., OH (U.S.))
Izvor:
5TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES - BOOK OF ABSTRACTS, 2022, 3-3Kolekcije
Institucija/grupa
Mašinski fakultetTY - CONF AU - Spalević, Miodrag PY - 2022 UR - https://machinery.mas.bg.ac.rs/handle/123456789/5147 AB - The estimation of the quadrature error of a Gauss quadrature rule when applied to the approximation of an integral determined by a real-valued integrand and a real-valued nonnegative measure with support on the real axis is an important problem in scientific computing. Laurie [2] developed anti-Gauss quadrature rules as an aid to estimate this error. Under suitable conditions the Gauss and associated anti-Gauss rules give upper and lower bounds for the value of the desired integral. It is then natural to use the average of Gauss and anti-Gauss rules as an improved approximation of the integral. Laurie also introduced these averaged rules. More recently, the author derived new averaged Gauss quadrature rules that have higher degree of exactness for the same number of nodes as the averaged rules proposed by Laurie. In [2], [5], [3] stable numerical procedures for computation of the corresponding averaged Gaussian rules are proposed. An analogous procedure can be applied also for a more general class of weighted averaged Gaussian rules introduced in [1]. Those results are presented in [4]. Here we we give a survey of the quoted results, which are obtained jointly with L. Reichel (Kent State Univ., OH (U.S.)) C3 - 5TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES - BOOK OF ABSTRACTS T1 - Computation of Generalized Averaged Gaussian Quadrature Rules EP - 3 SP - 3 UR - https://hdl.handle.net/21.15107/rcub_machinery_5147 ER -
@conference{ author = "Spalević, Miodrag", year = "2022", abstract = "The estimation of the quadrature error of a Gauss quadrature rule when applied to the approximation of an integral determined by a real-valued integrand and a real-valued nonnegative measure with support on the real axis is an important problem in scientific computing. Laurie [2] developed anti-Gauss quadrature rules as an aid to estimate this error. Under suitable conditions the Gauss and associated anti-Gauss rules give upper and lower bounds for the value of the desired integral. It is then natural to use the average of Gauss and anti-Gauss rules as an improved approximation of the integral. Laurie also introduced these averaged rules. More recently, the author derived new averaged Gauss quadrature rules that have higher degree of exactness for the same number of nodes as the averaged rules proposed by Laurie. In [2], [5], [3] stable numerical procedures for computation of the corresponding averaged Gaussian rules are proposed. An analogous procedure can be applied also for a more general class of weighted averaged Gaussian rules introduced in [1]. Those results are presented in [4]. Here we we give a survey of the quoted results, which are obtained jointly with L. Reichel (Kent State Univ., OH (U.S.))", journal = "5TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES - BOOK OF ABSTRACTS", title = "Computation of Generalized Averaged Gaussian Quadrature Rules", pages = "3-3", url = "https://hdl.handle.net/21.15107/rcub_machinery_5147" }
Spalević, M.. (2022). Computation of Generalized Averaged Gaussian Quadrature Rules. in 5TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES - BOOK OF ABSTRACTS, 3-3. https://hdl.handle.net/21.15107/rcub_machinery_5147
Spalević M. Computation of Generalized Averaged Gaussian Quadrature Rules. in 5TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES - BOOK OF ABSTRACTS. 2022;:3-3. https://hdl.handle.net/21.15107/rcub_machinery_5147 .
Spalević, Miodrag, "Computation of Generalized Averaged Gaussian Quadrature Rules" in 5TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES - BOOK OF ABSTRACTS (2022):3-3, https://hdl.handle.net/21.15107/rcub_machinery_5147 .