mathematics and computer science, computable analysis is the study of mathematical analysis from the perspective of computability theory. It is concerned with...

the recursive numbers, effective numbers, computable reals, or recursive reals. The concept of a computable real number was introduced by Émile Borel...

In mathematics, computable measure theory is the part of computable analysis that deals with effective versions of measure theory. Jeremy Avigad (2012)...

of computability that can be imagined can compute only functions that are computable in the above sense. Before the precise definition of computable functions...

undecidable) if it is not computable. A subset S {\displaystyle S} of the natural numbers is computable if there exists a total computable function f {\displaystyle...

and infinitely large numbers. Computable analysis, the study of which parts of analysis can be carried out in a computable manner. Stochastic calculus –...

not a computable real number. The proof uses a particular fact about computable real numbers. If x were computable then there would be a computable function...

many results in reverse mathematics have corresponding results in computable analysis. In higher-order reverse mathematics, the focus is on subsystems...

sequence converges. These moduli are often employed in the study of computable analysis and constructive mathematics. If a sequence of real numbers x i {\displaystyle...

computable objects. After an initial section of the book, introducing computable analysis and leading up to an example of John Myhill of a computable...

business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical...

Multiple-agent system Parameterized complexity Process calculi Pi-calculus Hypercomputation Real computation Computable analysis Weihrauch reducibility...

Church–Turing thesis, which states that any function that is computable by an algorithm is a computable function. Although initially skeptical, by 1946 Gödel...

space that has a computable presentation. Such spaces are studied in effective descriptive set theory and in constructive analysis. In particular, standard...

of computable functions. It states that a function on the natural numbers can be calculated by an effective method if and only if it is computable by...

In computable analysis, Weihrauch reducibility is a notion of reducibility between multi-valued functions on represented spaces that roughly captures...

Computable Analysis. O. Bournez; M. L. Campagnolo; D. S. Graça & E. Hainry (Jun 2007). "Polynomial differential equations compute all real computable...

Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data...

is unknown whether the Mandelbrot set is computable in models of real computation based on computable analysis, which correspond more closely to the intuitive...

require the gales to be either computable or close to computable: A gale d is called constructive, c.e., or lower semi-computable if the numbers d ( σ ) {\displaystyle...

was an American mathematical logician who did pioneering work in computable analysis. Marian Boykan was born in 1928 in New York City; her parents were...

Malware analysis is the study or process of determining the functionality, origin and potential impact of a given malware sample such as a virus, worm...

specifically computability and set theory, an ordinal α {\displaystyle \alpha } is said to be computable or recursive if there is a computable well-ordering...

Indecomposability (intuitionistic logic), a principle in constructive analysis and in computable analysis Indecomposability of a polynomial in polynomial decomposition...

Computable general equilibrium (CGE) models are a class of economic models that use actual economic data to estimate how an economy might react to changes...

computability theory, a function f : R → R {\displaystyle f\colon \mathbb {R} \to \mathbb {R} } is sequentially computable if, for every computable sequence...

constructive analysis. Computable model theory a branch of model theory dealing with the relevant questions computability. Computability theory a branch...

Computable Document Format (CDF) is an electronic document format designed to allow authoring dynamically generated, interactive content. CDF was created...

and E. Hainry. Polynomial differential equations compute all real computable functions on computable compact intervals. Journal of Complexity, 23:317–335...

eigenvector of a symmetric matrix is not computable (in exact real arithmetic according to the definitions in computable analysis). This difficulty exists whenever...