The Schur complement is a key tool in the fields of linear algebra, the theory of matrices, numerical analysis, and statistics. It is defined for a block...

In numerical analysis, the Schur complement method, named after Issai Schur, is the basic and the earliest version of non-overlapping domain decomposition...

are conformable with them for partitioning. Furthermore, A and the Schur complement of A in P: P/A = D − CA−1B must be invertible. Equivalently, by permuting...

Schur: Schur algebra Schur complement Schur index Schur indicator Schur multiplier Schur orthogonality relations Schur polynomial Schur product Schur...

In mathematics, Schur's lemma is an elementary but extremely useful statement in representation theory of groups and algebras. In the group case it says...

conjecture Schur complement method Schur complement Schur-convex function Schur decomposition Schur functor Schur index Schur's inequality Schur's lemma (from...

G} has a complement in G {\displaystyle G} . Moreover if either N {\displaystyle N} or G / N {\displaystyle G/N} is solvable then the Schur–Zassenhaus...

proved with stronger conditions on the blocks, for instance, using the Schur complement. A general quadratic form f ( x ) {\displaystyle f(\mathbf {x} )} on...

(sometimes called an antonym) Complement (group theory) Complementary subspaces Orthogonal complement Schur complement Complement (complexity), relating to...

matrix. The result is named after Issai Schur (Schur 1911, p. 14, Theorem VII) (note that Schur signed as J. Schur in Journal für die reine und angewandte...

-j}=X_{j}^{T}X_{-j},r_{-j,j}=X_{-j}^{T}X_{j},r_{-j,-j}=X_{-j}^{T}X_{-j}} . By using Schur complement, the element in the first row and first column in r − 1 {\displaystyle...

differences, the discretization of the Poincaré–Steklov operator is the Schur complement obtained by eliminating all degrees of freedom inside the domain. Note...

mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one...

where S := B ∗ A − 1 B {\displaystyle S:=B^{*}A^{-1}B} denotes the Schur complement. Since S {\displaystyle S} is symmetric positive-definite, we can apply...

) = {\displaystyle (D-CA^{-1}B)=} a much smaller matrix called the Schur complement of A {\displaystyle A} . This is the FKF method that may make it computationally...

using either the Leibniz formula or a factorization involving the Schur complement, is det ( A 0 C D ) = det ( A ) det ( D ) = det ( A B 0 D ) . {\displaystyle...

{In} (H_{11})+\mathrm {In} (H/H_{11})} where H/H11 is the Schur complement of H11 in H: H / H 11 = H 22 − H 12 ∗ H 11 − 1 H 12 . {\displaystyle...

differential equations as the capacitance matrix. Sherman–Morrison formula Schur complement Matrix determinant lemma, formula for a rank-k update to a determinant...

K Y | X {\displaystyle \operatorname {K} _{\mathbf {Y|X} }} is the Schur complement of K X X {\displaystyle \operatorname {K} _{\mathbf {XX} }} in Σ {\displaystyle...

{A} :=\mathbf {D} -\mathbf {C} \mathbf {A} ^{-1}\mathbf {B} } is the Schur complement of A. (A must be square, so that it can be inverted. Furthermore, A...

matrix Σ ¯ {\displaystyle {\overline {\boldsymbol {\Sigma }}}} is the Schur complement of Σ22 in Σ. That is, the equation above is equivalent to inverting...

and Boyd, Edinburgh, fourth edition, 1939. Zhang, Fuzhen, ed. The Schur complement and its applications. Vol. 4. Springer Science & Business Media, 2006...

worked in linear algebra and matrix theory. She gave the name to Schur complements and is the namesake of the Haynsworth inertia additivity formula....

decomposition Higher-order singular value decomposition Schur decomposition Schur complement Haynsworth inertia additivity formula Matrix equivalence...

equivalent network with one less node. The equivalence follows from the Schur complement identity applied to the Kirchhoff matrix of the network. The equivalent...

matrix D − C A − 1 B {\displaystyle D-CA^{-1}B\,} is known as the Schur complement of A relative to [ A B C D ] . {\displaystyle {\begin{bmatrix}A&B\\C&D\end{bmatrix}}...

translates the original matrix entries to the reduced matrix entries. Schur complement Power-flow study Caliskan, Sina Yamac; Tabuada, Paulo (2014). "Towards...

the rest constrained. Model order reduction Finite element method Schur complement - arising in the field of linear algebra when performing a block Gaussian...

iteration for the iterative solution of the equations arising from the Schur complement method. This continuous iteration can be discretized by the finite...

in the interiors of the subdomain, thus reducing the problem to the Schur complement on the subdomain interface. Since the BDD preconditioner involves the...