of Schur complements to matrixidentities and presents an extension of the Sherman-Morrison-Woodbury for-mula, which includes in a lot of matrix identities, such as Hua’s identity andits extensions.Keywords: Sherman-Morrison-Woodbury formula, Hua’s identity, SchurcomplementAMS subject classifications...
Keywords:Sherman-Morrison-Woodburyformula,Hua’sidentity,Schur complement AMSsubjectclassifications.15A45,15A48,15A24 1Introduction Thewell-knownmatrixidentity (A+UV ∗ ) −1 =A −1 −A −1 U(I+V ∗ A −1 U) −1 V ∗ A −1 ,(1) iacalledtobetheSherman-Morrison-Woodb...
The coupling is based on an exact linear algebra identity known as the Sherman-Morrison-Woodbury (SMW) formula. One advantage of this approach is that the FEM matrices are not modified. This is important if a fast “black-box” solver is available for the FEM matrices, these solvers ...
from scratch. The Sherman–Morrison–Woodbury formula is straightforward to verify, by showing that the product of the two sides is the identity matrix. How can the formula be derived in the first place? Consider any two matrices and such that and are both defined. The associative law for ma...