- Cite this article as:
- Rutishauser, H. Journal of Applied Mathematics and Physics (ZAMP) (1954) 5: 233. doi:10.1007/BF01600331
The quotient-difference (=QD) algorithm developed by the author may be considered as an extension ofBernoulli's method for solving algebraic equations. WhereasBernoulli's method gives the dominant root as the limit of a sequence of quotientsq 1 (v) =s 1 (v+1) /s 1 (v) formed from a certain numerical sequences 1 (v) , the QD-algorithm gives (under certain conditions) all the rootsλ σ as the limits of similiar quotient sequencesq σ (v) =s σ (v+1) /s σ (v) . Close relationship exists between this method and the theory of continued fractions. In fact the QD-algorithm permits developing a function given in the form of a power series into a continued fraction in a remarkably simple manner.
In this paper only the theoretical aspects of the method are discussed. Practical applications will be discussed later.