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Toeplitz matrix techniques and convergence of complex weight Padé approximants

✍ Scribed by Alphonse P. Magnus

Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
981 KB
Volume
19
Category
Article
ISSN
0377-0427

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✦ Synopsis

One considers diagonal Pad~ approximants about m of functions of the form

where w is an integrable, possibly complex-valued, function defined on [-1, 1].

Convergence of the sequence of diagonal Pad4 approximants towards f is established under the condition that there exists a weight ~o, positive almost everywhere on [ -1, 1], such that g(x) = w(x)/,o (x) is continuous and not vanishing on [ -1, 1].

The rate of decrease of the error is also described. The proof proceeds by establishing the link between the Pad6 denominators and the orthogonal polynomials related to ~o, in terms of the Toeplitz matrix of symbol g(cos 0).

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