Name
Abstract | ||
|---|---|---|
AbstractIt is well-known that the remaining term of a n-point Gaussian quadrature depends on the -order derivative of the integrand function. Discounting the fact that calculating a -order derivative requires a lot of differentiation, the main problem is that an error bound for a n-point Gaussian quadrature is only relevant for a function that is times differentiable, a rather stringent condition. In this paper, by defining some specific linear kernels, we resolve this problem and obtain new error bounds involving only the first derivative of the weighted integrand function for all Gaussian weighted quadrature rules whose nodes and weights are pre-assigned over a finite interval. The advantage of using linear kernels is that their -norm, -norm, maximum and minimum can easily be computed. Three illustrative examples are given in this direction. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1080/00207160.2015.1067307 | Periodicals |
Keywords | Field | DocType |
Gaussian quadratures, error bounds, linear kernels, orthogonal polynomials, weight function | Gauss–Kronrod quadrature formula,Mathematical optimization,Mathematical analysis,Tanh-sinh quadrature,Clenshaw–Curtis quadrature,Gaussian,Quadrature (mathematics),Gauss–Jacobi quadrature,Gaussian quadrature,Gaussian function,Mathematics | Journal |
Volume | Issue | ISSN |
93 | 9 | 0020-7160 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mohammad Masjed-Jamei | 1 | 15 | 8.03 |
| I. Area | 2 | 4 | 3.35 |