Name
Title | ||
|---|---|---|
Quadratures associated with pseudo-orthogonal rational functions on the real half line with poles in [-∞, 0]. |
Abstract | ||
|---|---|---|
We consider a positive measure on [0,~) and a sequence of nested spaces @?"0@?@?"1@?@?"2... of rational functions with prescribed poles in [-~,0]. Let {@f"k}"k"="0^~, with @f"0@?@?"0 and @f"k@?@?"k@?@?"k"-"1, k=1,2,... be the associated sequence of orthogonal rational functions. The zeros of @f"n can be used as the nodes of a rational Gauss quadrature formula that is exact for all functions in @?"n@?@?"n"-"1, a space of dimension 2n. Quasi- and pseudo-orthogonal functions are functions in @?"n that are orthogonal to some subspace of @?"n"-"1. Both of them are generated from @f"n and @f"n"-"1 and depend on a real parameter @t. Their zeros can be used as the nodes of a rational Gauss-Radau quadrature formula where one node is fixed in advance and the others are chosen to maximize the subspace of @?"n@?@?"n"-"1 where the quadrature is exact. The parameter @t is used to fix a node at a preassigned point. The space where the quadratures are exact has dimension 2n-1 in both cases but it is in @?"n"-"1@?@?"n"-"1 in the quasi-orthogonal case and it is in @?"n@?@?"n"-"2 in the pseudo-orthogonal case. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.cam.2012.06.037 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
pseudo-orthogonal case,quasi-orthogonal case,quadrature formula,pseudo-orthogonal rational function,rational function,nested space,associated sequence,orthogonal rational function,rational gauss-radau quadrature formula,pseudo-orthogonal function,rational gauss,real half line,primary,numerical quadrature | Mathematical optimization,Combinatorics,Subspace topology,Mathematical analysis,Numerical integration,Half line,Quadrature (mathematics),Rational function,Gaussian quadrature,Mathematics | Journal |
Volume | Issue | ISSN |
237 | 1 | 0377-0427 |
Citations | PageRank | References |
2 | 0.39 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Adhemar Bultheel | 1 | 217 | 34.80 |
| Pablo GonzáLez-Vera | 2 | 100 | 17.26 |
| Erik Hendriksen | 3 | 11 | 2.06 |
| Olav NjåStad | 4 | 56 | 12.34 |