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The principal motivation for the Blum Shub Smale model of computability was precisely the kind of concern you raise in your question. In particular, the BSS machines provide a numerical model of computation using a random access machine concept, where the registers hold full-precision real numbers. The dynamicists had wanted a theoretical model of computability that would untangle the discrete computational effects, such as round-off error, from the computational analysis of numerical algorithms involving continuous quantities. The BSS model is provably different from the model of computable analysis.

The principal motivation for the Blum Shub Smale model of computability was precisely the kind of concern you raise in your question. In particular, the BSS machines provide a numerical model of computation using a random access machine concept, where the registers hold full-precision real numbers. The dynamicists had wanted a theoretical model of computability that would untangle the discrete computational effects, such as round-off error, from the computational analysis of numerical algorithms involving continuous quantities. They wanted to provide a formal setting in which to analyze issues such as stability and convergence of algorithms in a more continuous setting, where quantities would be represented with perfect precision, and the typical discrete computational issues would loom less large. The BSS model is provably different from the model of computable analysis.

My understanding is that the principal motivation for the Blum Shub Smale model of computability is precisely the kind of concern you raise in your question. The dynamicists wanted a theoretical model of computability that would untangle the discrete computational effects, such as round-off error, from the computational analysis of numerical algorithms involving continuous quantities. The BSS model is provably different from the model of computable analysis.

The principal motivation for the Blum Shub Smale model of computability was precisely the kind of concern you raise in your question. In particular, the BSS machines provide a numerical model of computation using a random access machine concept, where the registers hold full-precision real numbers. The dynamicists had wanted a theoretical model of computability that would untangle the discrete computational effects, such as round-off error, from the computational analysis of numerical algorithms involving continuous quantities. The BSS model is provably different from the model of computable analysis.

My understanding is that the principal motivation for the Blum Shub Smale model of computability is precisely the kind of concern you raise in your question. The dynamicists wanted a theoretical model of computability that would avoid the effects such as round-off error that had plagued a discrete computational implementation of a continuous algorithm. The BSS model is provably different from the model of computable analysis.

My understanding is that the principal motivation for the Blum Shub Smale model of computability is precisely the kind of concern you raise in your question. The dynamicists wanted a theoretical model of computability that would untangle the discrete computational effects, such as round-off error, from the computational analysis of numerical algorithms involving continuous quantities. The BSS model is provably different from the model of computable analysis.