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About: Computable analysis

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In mathematics and computer science, computable analysis is the study of mathematical analysis from the perspective of computability theory. It is concerned with the parts of real analysis and functional analysis that can be carried out in a computable manner. The field is closely related to constructive analysis and numerical analysis. The above motivating results have no counterpart in Bishop's constructive analysis. Instead, it is the stronger form of constructive analysis developed by Brouwer that provides a counterpart in constructive logic.

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  • In mathematics and computer science, computable analysis is the study of mathematical analysis from the perspective of computability theory. It is concerned with the parts of real analysis and functional analysis that can be carried out in a computable manner. The field is closely related to constructive analysis and numerical analysis. A notable result is that integration (in the sense of the Riemann integral) is computable. This might be considered surprising as an integral is (loosely speaking) an infinite sum. While this result could be explained by the fact that every computable function from to is uniformly continuous, the notable thing is that the modulus of continuity can always be computed without being explicitly given. A similarly surprising fact is that differentiation of complex functions is also computable, while the same result is false for real functions. The above motivating results have no counterpart in Bishop's constructive analysis. Instead, it is the stronger form of constructive analysis developed by Brouwer that provides a counterpart in constructive logic. (en)
  • 数学ならびに計算機科学において、計算可能解析学（けいさんかのうかいせきがく、英語: computable analysis）とは、計算可能性理論の観点から解析学を研究する分野である。これは計算可能な仕方で展開可能な実解析学や関数解析学の部分と関わる。この分野はや数値解析と密接に関係する。 (ja)
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  • 数学ならびに計算機科学において、計算可能解析学（けいさんかのうかいせきがく、英語: computable analysis）とは、計算可能性理論の観点から解析学を研究する分野である。これは計算可能な仕方で展開可能な実解析学や関数解析学の部分と関わる。この分野はや数値解析と密接に関係する。 (ja)
  • In mathematics and computer science, computable analysis is the study of mathematical analysis from the perspective of computability theory. It is concerned with the parts of real analysis and functional analysis that can be carried out in a computable manner. The field is closely related to constructive analysis and numerical analysis. The above motivating results have no counterpart in Bishop's constructive analysis. Instead, it is the stronger form of constructive analysis developed by Brouwer that provides a counterpart in constructive logic. (en)
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  • Computable analysis (en)
  • 計算可能解析学 (ja)
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