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Horner's method evaluates a polynomial using repeated bracketing: + + + + + = + (+ (+ (+ + (+)))). This method reduces the number of multiplications and additions to just Horner's method is so common that a computer instruction "multiply–accumulate operation" has been added to many computer processors, which allow doing the addition and multiplication operations in one combined step.
In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation.Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and Persian mathematicians. [1]
The common usage, much older than the general definition of functions between sets, is to not use double parentheses and to simply write f(x 1, x 2, …, x n). It is also common to abbreviate the n-tuple (x 1, x 2, …, x n) by using a notation similar to that for vectors, like boldface x, underline x, or overarrow x →. This article will use ...
Many authors use these two words interchangeably. A polynomial P in the indeterminate x is commonly denoted either as P or as P(x). Formally, the name of the polynomial is P, not P(x), but the use of the functional notation P(x) dates from a time when the distinction between a polynomial and the associated function was unclear. Moreover, the ...
Some authors, such as Serge Lang, [13] use "function" only to refer to maps for which the codomain is a subset of the real or complex numbers, and use the term mapping for more general functions. In the theory of dynamical systems , a map denotes an evolution function used to create discrete dynamical systems .
The function f(x) is called the integrand, the points a and b are called the limits (or bounds) of integration, and the integral is said to be over the interval [a, b], called the interval of integration. [18] A function is said to be integrable if its integral over its domain is finite. If limits are specified, the integral is called a ...
De Bruijn notation – notation using postfix modification functions; Domain theory – Study of certain posets giving denotational semantics for lambda calculus; Evaluation strategy – Rules for the evaluation of expressions in programming languages; Explicit substitution – The theory of substitution, as used in β-reduction
Piecewise functions can be defined using the common functional notation, where the body of the function is an array of functions and associated subdomains. A semicolon or comma may follow the subfunction or subdomain columns. [ 4 ]