Abstract
A new pivotal strategy for reducing storage and arithmetic operations in computing the inverse of a matrix is outlined. This algorithm uses recursive deletion and partition to generate an efficient structure. The optimal selection of rows and columns to be deleted (spikes) is greatly facilitated through the use of certain exclusion criteria. The algorithm produces significantly fewer fill-ins and requires significantly fewer operations than the alternative P3 and P4 algorithms for the product form of the inverse (PFI). It also produces satisfactory structures for problems for which P3 and P4 would generate zero pivots. Three variants of HP algorithm specifically tailored for the elimination form of the inverse (EFI) and for greater speed are also presented. The algorithm has been implemented on a CDC 6400 computer. Performance comparison on six sample problems is given.
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Lin, T.D., Mah, R.S.H. Hierarchical partition—a new optimal pivoting algorithm. Mathematical Programming 12, 260–278 (1977). https://doi.org/10.1007/BF01593792
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DOI: https://doi.org/10.1007/BF01593792