Name
Abstract | ||
|---|---|---|
Quadrature rules with maximal even trigonometric degree of exactness are considered. We give a brief historical survey on such quadrature rules. Special attention is given on an approach given by Turetzkii [A.H. Turetzkii, On quadrature formulae that are exact for trigonometric polynomials, East J. Approx. 11 (3) (2005) 337-359. Translation in English from Uchenye Zapiski, Vypusk 1 (149). Seria Math. Theory of Functions, Collection of papers, Izdatel'stvo Belgosuniversiteta imeni V.I. Lenina, Minsk, 1959, pp. 31-54]. The main part of the topic is orthogonal trigonometric systems on [0,2@p) (or on [-@p,@p)) with respect to some weight functions w(x). We prove that the so-called orthogonal trigonometric polynomials of semi-integer degree satisfy a five-term recurrence relation. In particular, we study some cases with symmetric weight functions. Also, we present a numerical method for constructing the corresponding quadratures of Gaussian type. Finally, we give some numerical examples. Also, we compare our method with other available methods. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.camwa.2008.07.024 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
trigonometric degree,recurrence relation,so-called orthogonal trigonometric polynomial,orthogonality,weights,available method,trigonometric polynomial,trigonometric orthogonal system,quadrature formula,trigonometric degree of exactness,numerical method,quadrature rules of gaussian type,a.h. turetzkii,numerical example,nodes,quadrature rule,trigonometric interpolation,orthogonal trigonometric system,weight function,satisfiability | Gauss–Kronrod quadrature formula,Proofs of trigonometric identities,Discrete mathematics,Mathematical optimization,Differentiation of trigonometric functions,Mathematical analysis,Clenshaw–Curtis quadrature,Trigonometric substitution,Gauss–Jacobi quadrature,Mathematics,Pythagorean trigonometric identity,Trigonometric integral | Journal |
Volume | Issue | ISSN |
56 | 11 | Computers and Mathematics with Applications |
Citations | PageRank | References |
2 | 0.56 | 10 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gradimir V. Milovanović | 1 | 45 | 11.62 |
| Aleksandar S. Cvetković | 2 | 19 | 4.62 |
| Marija P. Stanić | 3 | 11 | 2.61 |