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A direct search method of optimization that works moderately well for stochastic problems. It is based on evaluating a function at the vertices of a simplex, then iteratively ...

A sequence of n-tuples that fills n-space more uniformly than uncorrelated random points, sometimes also called a low-discrepancy sequence. Although the ordinary uniform ...

A set T of integers is said to be recursively enumerable if it constitutes the range of a recursive function, i.e., if there exists a recursive function that can eventually ...

A theory is decidable iff there is an algorithm which can determine whether or not any sentence r is a member of the theory.

Consider decomposition the factorial n! into multiplicative factors p_k^(b_k) arranged in nondecreasing order. For example, 4! = 3·2^3 (1) = 2·3·4 (2) = 2·2·2·3 (3) and 5! = ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method (MINRES) and ...

A spectral sequence is a tool of homological algebra that has many applications in algebra, algebraic geometry, and algebraic topology. Roughly speaking, a spectral sequence ...

Stationary iterative methods are methods for solving a linear system of equations Ax=b, where A is a given matrix and b is a given vector. Stationary iterative methods can be ...

A pair of closed form functions (F,G) is said to be a Wilf-Zeilberger pair if F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k). (1) The Wilf-Zeilberger formalism provides succinct proofs of ...

A mathematical procedure for finding the best-fitting curve to a given set of points by minimizing the sum of the squares of the offsets ("the residuals") of the points from ...