polynomial

(definition)

Definition: (1) Any function which is the sum of constants times powers of the argument: f(x)=Σ_i=0^k c_ix^p_i. (2) In complexity theory, the measure of computation, m(n) (usually execution time or memory space), is bounded by a polynomial function of the problem size, n. More formally m(n) = O(n^k).

See also logarithmic, linear, exponential.

Note: Strictly speaking, a linear function is a polynomial with the highest exponent being 1, and a logarithmic function is a polynomial with fractional exponents. However polynomial usually means exponents greater than 1.

Author: PEB

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Entry modified 26 April 2021.
HTML page formatted Mon Apr 26 09:29:23 2021.

Cite this as:
Paul E. Black, "polynomial", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 26 April 2021. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/polynomial.html