Matrix Inversion by Partitioning

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Abstract
Summary: A systematic discussion of partitioning as a tool for matrix inversion is presented, together with various methods and applications which have been of help in actual computations. New concepts are introduced, among them those of super-matrix and of square partitioning. The most usual type of partitioning, that into 2x2 sub-matrices, is discussed in detail, showing the orderly arrangement of the calculations in an auxiliary matrix. Further sections deal with matrices of the continuant type, and with special types of symmetry in the arrangement of the sub-matrices. The greatest advantage of the method of partitioning for the inversion of these types (as compared with the elimination method) lies in a considerable reduction in the number of arithmetical operations.

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