Abstract
Ergodic computational aspects of the Jacobi algorithm, a generalization to two dimensions of the continued fraction algorithm, are considered. By means of such computations the entropy of the algorithm is estimated to be 3.5. An approximation to the invariant measure of the transformation associated with the algorithm is obtained. The computations are tested by application to the continued fraction algorithm for which both entropy and the invariant measure are known.
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Work partly performed under the auspices of the U.S. Atomic Energy Commission while one of the authors (M.S.W.) was a faculty participant of the Associated Western Universities at Los Alamos Scientific Laboratory. The work was also supported in part by NSF grant GP-28313 to M. S. W.
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Beyer, W.A., Waterman, M.S. Ergodic computations with continued fractions and Jacobi's algorithm. Numer. Math. 19, 195–205 (1972). https://doi.org/10.1007/BF01404688
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DOI: https://doi.org/10.1007/BF01404688