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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.

Attributes	Values
rdf:type	book
rdfs:label	Computable analysis (en) 計算可能解析学 (ja)
rdfs:comment	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)
dcterms:subject	Constructivism (mathematics) Computable analysis Computability theory
Wikipage page ID	21535996 (xsd:integer)
Wikipage revision ID	1119014469 (xsd:integer)
Link from a Wikipage to another Wikipage	Modulus of continuity Constructivism (mathematics) Riemann integral Uniform norm Decidability (logic) Real analysis Compactness Complex analysis Computability Computability theory Computable function Continuous function Mathematical analysis Mathematics McGraw-Hill General topology Open sets Closed sets Equality (mathematics) Constructive analysis Stephen Cole Kleene Computable analysis Computability in Analysis and Physics Computer science Functional analysis Partial function Specker sequence Steve Simpson (mathematician) Cauchy's integral formula Total function Hausdorff space Heine–Borel theorem Errett Bishop Extreme value theorem Numerical analysis Discontinuous linear map Computability theory L. E. J. Brouwer Topos Differential calculus Discrete space Marian Pour-El Integral Real closed field Semidecidable Turing machine Numerical differentiation Uniformly continuous Springer-Verlag Constructive logic Real functions Complex functions Computable numbers
Link from a Wikipage to an external page	http://cca-net.de/
sameAs	Computable analysis Computable analysis Computable analysis Computable analysis
dbp:wikiPageUsesTemplate	dbt:No_footnotes dbt:Isbn
has abstract	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)
gold:hypernym	Study
prov:wasDerivedFrom	wikipedia-en:Computable_analysis?oldid=1119014469&ns=0
page length (characters) of wiki page	7779 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Computable_analysis
is Link from a Wikipage to another Wikipage of	List of computability and complexity topics Reverse mathematics Mandelbrot set Weihrauch reducibility Mathematical analysis Glossary of areas of mathematics Constructive analysis Constructive set theory Andrzej Grzegorczyk Computability in Analysis and Physics Computable measure theory Computable number Specker sequence History of logic QR algorithm Modulus of convergence Marian Pour-El Indecomposability (intuitionistic logic)
is foaf:primaryTopic of	wikipedia-en:Computable_analysis

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