Abstract
A. In these lectures, we are dealing with the explicite or implicite use of continued fractions for the numerical solution of a number of problems. This means, that we are dealing with algorithms related to continued fractions. Since continued fractions have a profound connection with a certain class of (infinite) matrices, and since in our algorithms necessarily the approximants of continued fractions, which correspond to finite segments of these matrices play a role, there is good reason to base our lectures on the matrix theory of continued fractions. In Part I, we give an introduction to concepts and notations, and derive the principal algorithms, which we subsume under the name rhombus algorithms.
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