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An algorithm that runs in polynomial time but that is not strongly polynomial is said to run in weakly polynomial time. [2] A well-known example of a problem for which a weakly polynomial-time algorithm is known, but is not known to admit a strongly polynomial-time algorithm, is linear programming.
In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients [1]: ch. 17 [2]: ch. 10 (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence.
In the analysis of algorithms, an enumeration algorithm (i.e., an algorithm for listing a large or infinite collection of structures) is said to have polynomial delay if the time between the output of any one structure and the next is bounded by a polynomial function of the input size, in the worst case. [1] Polynomial delay implies that the ...
[1] [2] The exponential response formula is applicable to non-homogeneous linear ordinary differential equations with constant coefficients if the function is polynomial, sinusoidal, exponential or the combination of the three. [2]
Elimination theory culminated with the work of Leopold Kronecker, and finally Macaulay, who introduced multivariate resultants and U-resultants, providing complete elimination methods for systems of polynomial equations, which are described in the chapter on Elimination theory in the first editions (1930) of van der Waerden's Moderne Algebra.
For example, the term 2x in x 2 + 2x + 1 is a linear term in a quadratic polynomial. The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial . Unlike other constant polynomials, its degree is not zero.
In mathematics, a polylogarithmic function in n is a polynomial in the logarithm of n, [1] () + () + + () +.The notation log k n is often used as a shorthand for (log n) k, analogous to sin 2 θ for (sin θ) 2.
M runs for polynomial time on all inputs; For all x in L, M outputs 1 with probability greater than or equal to 1/2; For all x not in L, M outputs 0; Alternatively, RP can be defined using only deterministic Turing machines. A language L is in RP if and only if there exists a polynomial p and deterministic Turing machine M, such that