(definition)

**Definition:**
(1) Any function which is the sum of constants times powers of the argument: f(x)=Σ_{i=0}^{k} c_{i}x^{pi}. (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.

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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