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42 relations: Adept (C++ library), Algebra, Analytic function, Arithmetic, Backpropagation, Chain rule, Checkpointing scheme, Computational complexity theory, Computer algebra, Concrete number, Coupling (computer programming), Derivative, Discretization, Dual number, Dual space, Expression (mathematics), Faà di Bruno's formula, Formal power series, Gradient, Gradient descent, Infinitesimal, Jacobian matrix and determinant, Machine learning, Mathematical optimization, Mathematics, NP-completeness, Numerical differentiation, Operational calculus, Operator overloading, Ordered pair, Polynomial, Real number, Round-off error, Seppo Linnainmaa, Shift operator, Smooth infinitesimal analysis, Society for Industrial and Applied Mathematics, Space–time tradeoff, Springer Science+Business Media, Stan (software), Tensor algebra, Unary operation.
Adept (C++ library)
Adept is a combined automatic differentiation and array software library for the C++ programming language.
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Algebra
Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
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Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
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Arithmetic
Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.
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Backpropagation
Backpropagation is a method used in artificial neural networks to calculate a gradient that is needed in the calculation of the weights to be used in the network.
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Chain rule
In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions.
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Checkpointing scheme
Checkpointing schemes are scientific computing algorithms uses in solving time dependent adjoint equation, as well as reverse mode automatic differentiation.
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Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
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Computer algebra
In computational mathematics, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects.
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Concrete number
A concrete number or numerus numeratus is a number associated with the things being counted, in contrast to an abstract number or numerus numerans which is a number as a single entity.
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Coupling (computer programming)
In software engineering, coupling is the degree of interdependence between software modules; a measure of how closely connected two routines or modules are;ISO/IEC/IEEE 24765:2010 Systems and software engineering — Vocabulary the strength of the relationships between modules.
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Discretization
In mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts.
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Dual number
In linear algebra, the dual numbers extend the real numbers by adjoining one new element ε with the property ε2.
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Dual space
In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.
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Expression (mathematics)
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
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Faà di Bruno's formula
Faà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives, named after, though he was not the first to state or prove the formula.
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Formal power series
In mathematics, a formal power series is a generalization of a polynomial, where the number of terms is allowed to be infinite; this implies giving up the possibility of replacing the variable in the polynomial with an arbitrary number.
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Gradient
In mathematics, the gradient is a multi-variable generalization of the derivative.
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Gradient descent
Gradient descent is a first-order iterative optimization algorithm for finding the minimum of a function.
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Infinitesimal
In mathematics, infinitesimals are things so small that there is no way to measure them.
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
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Machine learning
Machine learning is a subset of artificial intelligence in the field of computer science that often uses statistical techniques to give computers the ability to "learn" (i.e., progressively improve performance on a specific task) with data, without being explicitly programmed.
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Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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NP-completeness
In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.
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Numerical differentiation
In numerical analysis, numerical differentiation describes algorithms for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.
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Operational calculus
Operational calculus, also known as operational analysis, is a technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation.
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Operator overloading
In programming, operator overloading, sometimes termed operator ad hoc polymorphism, is a specific case of polymorphism, where different operators have different implementations depending on their arguments.
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Ordered pair
In mathematics, an ordered pair (a, b) is a pair of objects.
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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Round-off error
A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value due to rounding.
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Seppo Linnainmaa
Seppo Linnainmaa (born 1945 in Pori, Finland) is a Finnish mathematician and computer scientist.
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Shift operator
In mathematics, and in particular functional analysis, the shift operator also known as translation operator is an operator that takes a function to its translation.
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Smooth infinitesimal analysis
Smooth infinitesimal analysis is a modern reformulation of the calculus in terms of infinitesimals.
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Society for Industrial and Applied Mathematics
The Society for Industrial and Applied Mathematics (SIAM) is an academic association dedicated to the use of mathematics in industry.
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Space–time tradeoff
A space–time or time–memory trade-off in computer science is a case where an algorithm or program trades increased space usage with decreased time.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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Stan (software)
Stan is a probabilistic programming language for statistical inference written in C++.
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Tensor algebra
In mathematics, the tensor algebra of a vector space V, denoted T(V) or T(V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product.
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Unary operation
In mathematics, a unary operation is an operation with only one operand, i.e. a single input.
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Algorithmic differentiation, Auto derivative, Auto derivatives, Forward accumulation, Reverse accumulation.
References
[1] https://en.wikipedia.org/wiki/Automatic_differentiation
