Counter-examples to the Baker-Garnmel-Wills conjecture and patchwork convergence

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:179

Article; Proceedings Paper

Baker, GA

关键词: Pade approximants;    Baker-Gammel-Wills conjecture;    spurious poles;   

DOI  :  10.1016/j.cam.2004.09.031

来源: Elsevier

【 摘 要 】

I review some of the by now classic conjectures concerning the pointwise convergence of the diagonal Pade approximants and the very recent counter-examples to all of them. As the counter-examples all correspond to bounded associated continued fractions (Wall's family of complex, bounded J-matrices), I review and extend some of the known convergence results. I propose a new conjecture which I call the patchwork conjecture, which restores uniform convergence by means of the use of a finite number of infinite sequences of diagonal Pade approximants instead of just one as in the classic conjectures. (c) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free