Bi-orthogonality in rational approximation

✍ Scribed by A. Iserles; E.B. Saff

• Publisher: Elsevier Science
• Year: 1987
• Tongue: English
• Weight: 395 KB
• Volume: 19
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(87)80007-9

✦ Synopsis

The well-known connection between Pad6 approximants to Stieltjes functions and orthogonal polynomials is crucial in locating zeros and poles and in convergence theorems. In the present paper we extend similar types of analysis to more elaborate forms of approximation. It transpires that the link with orthogonal polynomials remains valid with regard to rational interpolants, whereas simultaneous Pad6 and Levin Sidi approximants yield themselves to analysis with bi-orthogonal polynomials.