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Numerical differentiation. Finite difference estimation of derivative. In numerical analysis, numerical differentiation algorithms estimate the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.
v. t. e. In mathematics, the derivative is a fundamental tool that quantifies the sensitivity of change of a function 's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
Axiom is a general-purpose computer algebra system. It has been in development since 1971 by IBM, and was originally named scratchpad. Richard Jenks originally headed it but over the years Barry Trager who then shaped the direction of the scratchpad project took over the project. It was eventually sold to the Numerical Algorithms Group (NAG ...
f ′ (x) A function f of x, differentiated once in Lagrange's notation. One of the most common modern notations for differentiation is named after Joseph Louis Lagrange, even though it was actually invented by Euler and just popularized by the former. In Lagrange's notation, a prime mark denotes a derivative.
Automatic differentiation exploits the fact that every computer calculation, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.) and elementary functions (exp, log, sin, cos, etc.). By applying the chain rule repeatedly to these operations, partial ...
Derivation (differential algebra) In mathematics, a derivation is a function on an algebra that generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or a field K, a K -derivation is a K - linear map D : A → A that satisfies Leibniz's law: More generally, if M is an A - bimodule, a K -linear map ...
Hessian automatic differentiation. In applied mathematics, Hessian automatic differentiation are techniques based on automatic differentiation (AD) that calculate the second derivative of an -dimensional function, known as the Hessian matrix . When examining a function in a neighborhood of a point, one can discard many complicated global ...
Adept is a combined automatic differentiation and array software library for the C++ programming language. The automatic differentiation capability facilitates the development of applications involving mathematical optimization. Adept is notable for having applied the template metaprogramming technique of expression templates to speed-up the ...