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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.
In chemical analysis, matrix refers to the components of a sample other than the analyte [1] of interest. The matrix can have a considerable effect on the way the analysis is conducted and the quality of the results are obtained; such effects are called matrix effects. [ 2 ]
An "almost" triangular matrix, for example, an upper Hessenberg matrix has zero entries below the first subdiagonal. Hollow matrix: A square matrix whose main diagonal comprises only zero elements. Integer matrix: A matrix whose entries are all integers. Logical matrix: A matrix with all entries either 0 or 1.
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 ]
An iterative method with a given iteration matrix is called convergent if the following holds lim k → ∞ C k = 0. {\displaystyle \lim _{k\rightarrow \infty }C^{k}=0.} An important theorem states that for a given iterative method and its iteration matrix C {\displaystyle C} it is convergent if and only if its spectral radius ρ ( C ...
The different notions of convergence capture different properties about the sequence, with some notions of convergence being stronger than others. For example, convergence in distribution tells us about the limit distribution of a sequence of random variables. This is a weaker notion than convergence in probability, which tells us about the ...
A rigid matrix protects emitters from being quenched, extending the lifetime of phosphoresce. [27] In this circumstance, α-CD and CB could be used, [28] [29] in which the phosphor is served as a guest to interact with the host. For example, 4-phenylpyridium derivatives interacted with CB, and copolymerize with acrylamide. The resulting polymer ...
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.
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