(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

An explanation of how quadratic and other polynomials got their names.

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 17 December 2004.

HTML page formatted Fri Feb 23 10:06:08 2018.

Cite this as:

Paul E. Black, "polynomial", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/polynomial.html