کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4634758 1340699 2007 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Computability on reals, infinite limits and differential equations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Computability on reals, infinite limits and differential equations
چکیده انگلیسی

We study a countable class of real-valued functions inductively defined from a basic set of trivial functions by composition, solving first-order differential equations and the taking of infinite limits. This class is the analytical counterpart of Kleene’s partial recursive functions. By counting the number of nested limits required to define a function, this class can be stratified by a potentially infinite hierarchy—a hierarchy of infinite limits. In the first meaningful level of the hierarchy, we have the extensions of classical primitive recursive functions. In the next level, we find partial recursive functions, and in the following level we find the solution to the halting problem.We use methods from numerical analysis to show that the hierarchy does not collapse, concluding that the taking of infinite limits can always produce new functions from functions in the previous levels of the hierarchy.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 191, Issue 2, 15 August 2007, Pages 353–371
نویسندگان
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