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The method is an extension of the method of matrix decomposition proposed by Buzbee et al. (SIAM J. Numer. Anal. 7 (1970)).
A method of matrix transformation is developed to solve the ill-condition problem in the even regions of dynamic instability of the column caused by inclusion of damping.
The PTI consists of two methods: the method of matrix exponential and the method of Riccati equations, both of which utilize the merit of 2N algorithm and guarantee high precise numerical results.
The method of matrix exponential follows the similar scheme proposed for initial value problem of ODEs, and uses the matrix exponential to link boundary conditions between the two points.
In the Section 3 Fig. 15 The method of matrix partition.
If a method of matrix updating emanates from some distance minimization problem, it can be fully adapted to homothetic testing (see Sect. 6).
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Whilst pyrolysis mass spectrometry was used for bacterial analysis in the past [15], current methods are based on electrospray-ionization (ESI-MS) [16,17] and the more popular method of matrix-assisted laser desorption ionization (MALDI-MS) [14,18 20].
However, some methods of matrix updating demonstrate an incorrigible failure of homothetic testing.
Two methods of matrix inversion are implemented, namely Gauss-Jordan and Cholesky decomposition.
In this article, we have considered four methods of matrix updating that can be used for handling the matrices with some negative entries, namely, Kuroda's, iWSD, iWSRD and GRAS (including mGRAS) methods.
Thus, one can assert that improved WSRD method has some advantage among the other methods of matrix updating in practically important situations when the initial matrix has some very small entries and some very large ones simultaneously (because of multiplicative nature of iWSRD objective function).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com