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• W2022900146 abstract "Abstract Most of the published methods for the calculation of the inverse of matrix graph theory methods take advantage of the structure of the graph to reorder the matrix, for easier inversion. This study presents a method for the inversion of a large sparse matrix by means of a signal flow graph, that is analogous to a process flowsheet, using the 1956 Mason formula [1], widely used in electrical engineering to calculate the gain of a complex electronic network. A new data structure, called path matrix, was developed to contain the full information about the one edge paths in the graph. Information about greater edge paths is added. All the cycles of the graph are identified and their signal values are calculated. The sets of nontouching cycles are identified and the calculation formula is applied. Sparse matrices with dimensions of 10–100 were tested. The program inverted all test matrices, even those that could not be inverted by the IMSL routine LINV2F, up to the limit of the expandability of the path matrix. However, due to the complexity of the algorithm, CPU times for inversion of large matrices are unacceptable, except for ill-conditioned matrices that other methods fail to invert. This inverse matrix of a linear process flowsheet can be calculated directly from the graph describing the process." @default.
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• W2022900146 date "1987-01-01" @default.
• W2022900146 modified "2023-09-27" @default.
• W2022900146 title "Inversion of sparse matrices by a method based on graph theory" @default.
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• W2022900146 doi "https://doi.org/10.1016/0098-1354(87)87019-9" @default.
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