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- W83007147 abstract "Abstract This paper describes a new approach to the solution of a linear sparse system A x = b of m simultaneous equations in m real or complex variables. The approach involves the decomposition of the system into a hierarchy of subsystems. Given this decomposition, the purpose of the algorithm is first to generate a partial representation [A−1] of the inverse A−1, and then to compute A−1 b using [A−1]. This ‘pre-inverse’ [A−1] has four important properties: 1. Given [A−1], the task of solving A x = b is approximately equivalent to that of solving a triangular system of same size and density. 2. The number of coefficients in [A−1] in general is much smaller than the number of non-zero coefficients in A−1. 3. The various lists making up [A−1] are largely independent of each other, and thus to that extent may be generated independently, possibly on parallel processors. 4. [A−1] is generated by a recursive process. This means that some of the lists in [A−1] may be generated from other lists of [A−1]. The construction of [A−1] is thus efficient, simple and elegant." @default.
- W83007147 created "2016-06-24" @default.
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- W83007147 date "1984-01-01" @default.
- W83007147 modified "2023-09-26" @default.
- W83007147 title "A DECOMPOSITION ALGORITHM FOR SOLVING SPARSE SYSTEMS OF SIMULTANEOUS EQUATIONS" @default.
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- W83007147 doi "https://doi.org/10.1016/b978-0-08-030156-3.50022-9" @default.
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