- 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 quotientsq1(v)=s1(v+1)/s1(v) formed from a certain numerical sequences1(v), the QD-algorithm gives (under certain conditions) all the rootsλσ as the limits of similiar quotient sequencesqσ(v)=sσ(v+1)/sσ(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.