Computable analysis: an introduction
Computable analysis: an introduction
Weakly computable real numbers
Journal of Complexity
Recursively enumerable reals and Chaitin &OHgr; numbers
Theoretical Computer Science
Closure Properties of Real Number Classes under CBV Functions
Theory of Computing Systems
Divergence bounded computable real numbers
Theoretical Computer Science - Real numbers and computers
Finitely Bounded Effective Computability
Electronic Notes in Theoretical Computer Science (ENTCS)
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A real number is called computably approximable if there is a computable sequence of rational numbers which converges to it. To investigate the complexity of computably approximable real numbers, we can consider the converging speed of the sequences. In this paper we introduce a natural way to measure the converging speed by counting the jumps of certain size appeared after certain stages. The number of this big jumps can be bounded by a bounding function. For different choice of bounding functions, we introduce various classes of real numbers with different approximation quality and discuss their mathematical properties as well as computability theoretical properties.