Glasnik Matematicki, Vol. 48, No. 2 (2013), 231-247.

HOUSEHOLDER'S APPROXIMANTS AND CONTINUED FRACTION EXPANSION OF QUADRATIC IRRATIONALS

Vinko Petričević

Abstract.   There are numerous methods for rational approximation of real numbers. Continued fraction convergent is one of them and Newton's iterative method is another one. Connections between these two approximation methods were discussed by several authors. Householder's methods are generalisation of Newton's method. In this paper, we will show that for these methods analogous connection with continued fractions hold.

2010 Mathematics Subject Classification.   11A55.

Key words and phrases.   Continued fractions, Householder's iterative methods.

DOI: 10.3336/gm.48.2.02

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