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A new Chebyshev family with applications to Abel equations

✍ Scribed by Armengol Gasull; Chengzhi Li; Joan Torregrosa


Book ID
113699130
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
140 KB
Volume
252
Category
Article
ISSN
0022-0396

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When two or more branches of a function merge, the Chebyshev series of u(Ξ») will converge very poorly with coefficients a n of T n (Ξ») falling as O(1/n Ξ± ) for some small positive exponent Ξ±. However, as shown in [J.P. Boyd, Chebyshev polynomial expansions for simultaneous approximation of two branc

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To search a given real interval for roots, our algorithm is to replace \(f(\lambda)\) by \(f_{N}(\lambda)\), its \(N\)-term Chebyshev expansion on the search interval \(\lambda \in\left[\lambda_{\min }, \lambda_{\max }\right]\), and compute the roots of this proxy. This strategy is efficient if and