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Down arrow notation is an inverse of the Knuth up-arrow notation defined by evn = lnn (1) evvn = ln^*n (2) evvvn = ln^(**)n, (3) where ln^*n is the number of times the ...

A quadrature (numerical integration) algorithm which has a number of desirable properties.

Numerical stability refers to how a malformed input affects the execution of an algorithm. In a numerically stable algorithm, errors in the input lessen in significance as ...

An algorithm for computing an Egyptian fraction (Stewart 1992).

The security of a cryptosystem must not depend on keeping the cryptographic algorithm secret.

An algorithm for finding roots for quartic equations with complex roots.

The analytic summation of a hypergeometric series. Powerful general techniques of hypergeometric summation include Gosper's algorithm, Sister Celine's method, Wilf-Zeilberger ...

A recursive function devised by I. Takeuchi in 1978 (Knuth 1998). For integers x, y, and z, it is defined by (1) This can be described more simply by t(x,y,z)={y if x<=y; {z ...

A labeled binary tree containing the labels 1 to n with root 1, branches leading to nodes labeled 2 and 3, branches from these leading to 4, 5 and 6, 7, respectively, and so ...

A ring without zero divisors in which an integer norm and an associated division algorithm (i.e., a Euclidean algorithm) can be defined. For signed integers, the usual norm ...