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When successive powers of a matrix T become small (that is, when all of the entries of T approach zero, upon raising T to successive powers), the matrix T converges to the zero matrix. A regular splitting of a non-singular matrix A results in a convergent matrix T. A semi-convergent splitting of a matrix A results in a semi-convergent matrix T.
A matrix effect value of less than 100 indicates suppression, while a value larger than 100 is a sign of matrix enhancement. An alternative definition of matrix effect utilizes the formula: M E = 100 ( A ( e x t r a c t ) A ( s t a n d a r d ) ) − 100 {\displaystyle ME=100\left({\frac {A(extract)}{A(standard)}}\right)-100}
Synonym for binary matrix or logical matrix. Alternant matrix: A matrix in which successive columns have a particular function applied to their entries. Alternating sign matrix: A square matrix with entries 0, 1 and −1 such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. Anti-diagonal ...
If an equation can be put into the form f(x) = x, and a solution x is an attractive fixed point of the function f, then one may begin with a point x 1 in the basin of attraction of x, and let x n+1 = f(x n) for n ≥ 1, and the sequence {x n} n ≥ 1 will converge to the solution x.
In chemistry a convergent synthesis is a strategy that aims to improve the efficiency of multistep synthesis, most often in organic synthesis.In this type of synthesis several individual pieces of a complex molecule are synthesized in stage one, and then in stage two these pieces are combined to form the final product. [1]
Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2). In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite.
In quantum mechanics, a density matrix (or density operator) is a matrix that describes an ensemble [1] of physical systems as quantum states (even if the ensemble contains only one system). It allows for the calculation of the probabilities of the outcomes of any measurements performed upon the systems of the ensemble using the Born rule .
Ewald summation is a special case of the Poisson summation formula, replacing the summation of interaction energies in real space with an equivalent summation in Fourier space. In this method, the long-range interaction is divided into two parts: a short-range contribution, and a long-range contribution which does not have a singularity.