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The expression is a regular splitting of A if and only if B −1 ≥ 0 and C ≥ 0, that is, B −1 and C have only nonnegative entries. If the splitting is a regular splitting of the matrix A and A −1 ≥ 0, then ρ(T) < 1 and T is a convergent matrix. Hence the method converges. [12] [13]
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}
A matrix with all entries either 0 or 1. Synonym for (0,1)-matrix, binary matrix or Boolean matrix. Can be used to represent a k-adic relation. Markov matrix: A matrix of non-negative real numbers, such that the entries in each row sum to 1. Metzler matrix: A matrix whose off-diagonal entries are non-negative. Monomial matrix
In a generator, the molecular formula is the basic input. If fragments are obtained from the experimental data, they can also be used as inputs to accelerate structure generation. The first structure generators were versions of graph generators modified for chemical purposes.
Matrix congruence is an equivalence relation. Matrix congruence arises when considering the effect of change of basis on the Gram matrix attached to a bilinear form or quadratic form on a finite-dimensional vector space: two matrices are congruent if and only if they represent the same bilinear form with respect to different bases.
Computer-assisted organic synthesis software is a type of application software used in organic chemistry in tandem with computational chemistry to help facilitate the tasks of designing, predicting, and producing chemical reactions. CAOS aims to identify a series of chemical reactions which, from a starting compound, can produce a desired molecule.
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.
Notice that the 1/2 here is essential—there is an example of a 1/2-Hölder functions due to Hardy and Littlewood, [14] which do not belong to the Wiener algebra. Besides, this theorem cannot improve the best known bound on the size of the Fourier coefficient of a α-Hölder function—that is only O ( 1 / n α ) {\displaystyle O(1/n^{\alpha ...