caa a22 4500 475838947 CHVBK 20180406123856.0 cr unu---uuuuu 170329e20000501xx s 000 0 eng 10.1023/A:1006414501573 doi (NATIONALLICENCE)springer-10.1023/A:1006414501573 Lorentzen Lisa Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491, Trondheim, Norway. e-mail aut Ideas from Continued Fraction Theory Extended to Padé Approximation and Generalized Iteration [Elektronische Daten] [Lisa Lorentzen] This is a survey of some basic ideas in the convergence theory for continued fractions, in particular value sets, general convergence and the use of modified approximants to obtain convergence acceleration and analytic continuation. The purpose is to show how these ideas apply to some other areas of mathematics. In particular, we introduce {w k }-modifications and general convergence for sequences of Padé approximants. Kluwer Academic Publishers, 2000 continued fraction nationallicence Padé approximation nationallicence convergence nationallicence general convergence nationallicence convergence acceleration nationallicence generalized iteration nationallicence self-mappings nationallicence Acta Applicandae Mathematica Kluwer Academic Publishers 61/1-3(2000-05-01), 185-206 0167-8019 61:1-3<185 2000 61 10440 https://doi.org/10.1023/A:1006414501573 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1006414501573 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lorentzen Lisa Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491, Trondheim, Norway. e-mail aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 61/1-3(2000-05-01), 185-206 0167-8019 61:1-3<185 2000 61 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer