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Convergence Rates of Padé and Padé-Type Approximants

✍ Scribed by Amiran Ambroladze; Hans Wallin

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
356 KB
Volume
86
Category
Article
ISSN
0021-9045

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✦ Synopsis

A comparison is made between Pade and Pade -type approximants. Let Q n be the n th orthonormal polynomial with respect to a positive measure + with compact support in C. We show that for functions of the form

where w is an analytic function on the support of +, Pade -type approximants with denominator Q n give a successful and, in general, better approximation procedure than Pade approximation.

1996 Academic Press, Inc.

Q2. How easily and within what computational accuracy may the approximants be constructed? Q3. Which is the theoretical accuracy (rate of convergence)?

We want to compare Pade and Pade -type approximants in a discussion on these three questions. First, however, we define our approximants. We article no. 0072 310

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