D. Teichroew
ABSTRACT
Three numerical methods for evaluating continued fractions are discussed. An Arithmetic example is given for each method. A comparison is made of the speed of convergence of power series expansions and continued fraction expansions for several functions. Recommendations are made for the most efficient method of evaluating continued fractions for different types of computing machines.
Index Terms
- Use of continued fractions in high-speed computing
Recommendations
On the Use of Continued Fractions for Digital Computer Arithmetic
Recently, there has been some interest in the use of continued fractions for digital hardware calculations. We require that the coefficients of the continued fractions be integral powers of 2 and, therefore, well-known continued fraction expansions of ...
Matrix-valued continued fractions
We discuss the properties of matrix-valued continued fractions based on Samelson inverse. We begin to establish a recurrence relation for the approximants of matrix-valued continued fractions. Using this recurrence relation, we obtain a formula for the ...
A theorem on divergence in the general sense for continued fractions
If the odd and even parts of a continued fraction converge to different values, the continued fraction may or may not converge in the general sense. We prove a theorem which settles the question of general convergence for a wide class of such continued ...
Comments