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Weighted fit by orthonormal polynomials

✍ 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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✦ 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.


πŸ“œ SIMILAR VOLUMES


Orthonormal polynomials with generalized
✍ T. Kasuga; R. Sakai πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 344 KB

We consider a certain generalized Freud-type weight W 2 rQ Γ°xÞ ΒΌ jxj 2r expðÀ2QΓ°xÞÞ; where r4 Γ€ 1 2 and Q : R-R is even and continuous, Q 0 is continuous, Q 0 40 in Γ°0; NÞ; and Q 00 is continuous in Γ°0; NÞ: Furthermore, Q satisfies further conditions. Recently, Levin and Lubinsky have studied the se

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✍ D.S. Lubinsky πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 552 KB

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

Approximation by weighted polynomials
✍ David Benko πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 262 KB

It is proven that if xQ 0 Γ°xÞ is increasing on Γ°0; ΓΎNÞ and wΓ°xÞ ΒΌ expðÀQΓ°xÞÞ is the corresponding weight on Β½0; ΓΎNÞ; 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 :