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On Stieltjes polynomials and Gauss-Kronrod quadrature
| Content Provider | Semantic Scholar |
|---|---|
| Author | Peherstorfer, Franz |
| Copyright Year | 1990 |
| Abstract | Let D be a real function such that D(z) is analytic and D(z) ± 0 for \z\ < 1. Furthermore, put W(x) = \J\ x2\D(e'v)\2 , x = costp , tp e [0, 71 ], and denote by pn(', rV) the polynomial which is orthogonal on [-1, +1] to Pn_[ (P„_! denotes the set of polynomials of degree at most n 1 ) with respect to W . In this paper it is shown that for each sufficiently large n the polynomial En+X(-, W) (called the Stieltjes polynomial) of degree n + \ which is orthogonal on [-1,-1-1] to Pn with respect to the sign-changing function pn('> W)W has n + 1 simple zeros in (-1,1) and that the interpolation quadrature formula (called the Gauss-Kronrod quadrature formula) based on nodes which are the In + 1 zeros of En+l(-, W)pn(-, IV) has all weights positive. |
| Starting Page | 649 |
| Ending Page | 664 |
| Page Count | 16 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0025-5718-1990-1035940-8 |
| Volume Number | 55 |
| Alternate Webpage(s) | http://www.ams.org/journals/mcom/1990-55-192/S0025-5718-1990-1035940-8/S0025-5718-1990-1035940-8.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0025-5718-1990-1035940-8 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
