We consider a certain generalized Freud-type weight W 2 rQ Γ°xΓ ΒΌ jxj 2r expΓ°Γ2QΓ°xΓΓ; where r4 Γ 1 2 and Q : R-R is even and continuous, Q 0 is continuous, Q 0 40 in Γ°0; NΓ; and Q 00 is continuous in Γ°0; NΓ: Furthermore, Q satisfies further conditions. Recently, Levin and Lubinsky have studied the se
Weighted fit by orthonormal polynomials
β Scribed by E. Rosato; M. Vigilante; N. De Cesare; E. Perillo; G. Spadaccini
- Book ID
- 103044821
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 346 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0010-4655
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β¦ Synopsis
The fitting technique by orthonormal polynomials and Forsythe's recurrence relationship, generalized in order to take into account experimental errors, are discussed. Comparison is made between orthonormal and standard fits to point out the improvements on the latter, mainly from a computational point of view.
π SIMILAR VOLUMES
R ---\* R is even, and "smooth," and of faster than polynomial growth at infinity. For example, we consider Q(x) = exp k/(]xla), a > 1, where expk = exp(exp(.., exp(... ))) denotes the k th iterated exponential. Weights of the form W 2 for such W are often called ErdSs weights. We compute the growth
It is proven that if xQ 0 Γ°xΓ is increasing on Γ°0; ΓΎNΓ and wΓ°xΓ ΒΌ expΓ°ΓQΓ°xΓΓ is the corresponding weight on Β½0; ΓΎNΓ; then every continuous function that vanishes outside the support of the extremal measure associated with w can be uniformly approximated by weighted polynomials of the form w n P n :