Continued fractions

  • Adhemar Bultheel
Part of the Operator Theory: Advances and Applications book series (OT, volume 27)


In the previous chapter we introduced a number of Padé approximants of different nature. The numerators and denominators of those approximants were all generated by the fundamental recursion (3.6). We have seen in chapters 3 and 4 that in (3.6) S n can be replaced by one of P n , Qn, R n , A n , B(p) n , zU n-1 or Vn-1, provided the appropriate initial conditions are used. It was explained in chapter 2 how Moebius transforms, like the one represented by (3.6), are related to continued fractions. We use this to show in this chapter how CFs can be obtained having for their successive convergents the different Padé-like approximants of chapter 4.


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Copyright information

© Birkhäuser Verlag Basel 1987

Authors and Affiliations

  • Adhemar Bultheel
    • 1
  1. 1.Dept. Computer ScienceK. U. LeuvenLeuven-HeverleeBelgium

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