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A mental device used to aid memorization. Common mnemonics for mathematical constants such as e and pi consist of sentences in which the number of letters in each word give ...

The rook numbers r_k^((m,n)) of an m×n board are the number of subsets of size k such that no two elements have the same first or second coordinate. In other word, it is the ...

The conjugate gradient method is not suitable for nonsymmetric systems because the residual vectors cannot be made orthogonal with short recurrences, as proved in Voevodin ...

Chebyshev iteration is a method for solving nonsymmetric problems (Golub and van Loan 1996, §10.1.5; Varga, 1962, Ch. 5). Chebyshev iteration avoids the computation of inner ...

Taking a connected graph or network with a high graph diameter and adding a very small number of edges randomly, the diameter tends to drop drastically. This is known as the ...

A rook polynomial is a polynomial R_(m,n)(x)=sum_(k=0)^(min(m,n))r_kx^k (1) whose number of ways k nonattacking rooks can be arranged on an m×n chessboard. The rook ...

Parallel computing is the execution of a computer program utilizing multiple computer processors (CPU) concurrently instead of using one processor exclusively. Let T(n,1) be ...

The conjugate gradient method is an algorithm for finding the nearest local minimum of a function of n variables which presupposes that the gradient of the function can be ...

Conway's knot is the prime knot on 11 crossings with braid word sigma_2^3sigma_1sigma_3^(-1)sigma_2^(-2)sigma_1sigma_2^(-1)sigma_1sigma_3^(-1). The Jones polynomial of ...

A simple way to describe a knot projection. The advantage of this notation is that it enables a knot diagram to be drawn quickly. For an oriented alternating knot with n ...