Schur Complement
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Schur Complement

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High Quality Content by WIKIPEDIA articles! In linear algebra and the theory of matrices, the Schur complement of a matrix block (i.e., a submatrix within a larger matrix) is defined as follows. Suppose A, B, C, D are respectively p×p, p×q, q×p and q×q matrices, and D is invertible. It is named after Issai Schur who used it to prove Schur's lemma, although it had been used previously. In numerical analysis, the Schur complement method is the basic and the earliest version of non-overlapping domain decomposition method, also called iterative substructuring. A finite element problem is split...