Results 21 to 30 of about 12,699 (134)
Some inequalities on generalized Schur complements
Linear Algebra and its Applications, 1999 Let \(A=[A_{ij}]\) denote a block matrix of order two with square diagonal blocks. The generalized Schur complement \(S_1(A)\) of \(A_{11}\) is defined by \(S_1(A)=A_{22} -A_{21}A^+_{11} A_{12}\) where \(A^+_{11}\) denotes the Moore-Penrose pseudoinverse of \(A_{11}\) so that \(S_1(A)\) is defined also for singular matrices. For a Hermitian matrix \(A\)
Wang, Bo-Ying +2 more
openaire +1 more source
The Forward Order Law for Least Squareg-Inverse of Multiple Matrix Products
Mathematics, 2019 The generalized inverse has many important applications in the aspects of the theoretic research of matrices and statistics. One of the core problems of the generalized inverse is finding the necessary and sufficient conditions of the forward order laws ...
Zhiping Xiong, Zhongshan Liu
doaj +1 more source
Algebraic Multigrid for Disordered Systems and Lattice Gauge Theories [PDF]
, 2000 The construction of multigrid operators for disordered linear lattice operators, in particular the fermion matrix in lattice gauge theories, by means of algebraic multigrid and block LU decomposition is discussed.
Best, Christoph
core +2 more sources
Generalized Schur complements and oblique projections
Linear Algebra and its Applications, 2002 Let \(A\in L(\mathcal{H})\) be a positive operator, and \(\varphi\) be a closed subspace of the Hilbert space \(\mathcal{H}\). The shorted operator of \(A\) by \(\varphi\) is defined by \(A_{/\varphi}=\max\{X\in L(\mathcal{H})\;:\;0\leq X\leq A \text{ and } R(X)\subseteq \varphi^{\perp}\} \). A pair \((A,\varphi)\) is called compatible if the set \(\{Q\
Corach, Gustavo +2 more
openaire +3 more sources
IEEE Access, 2019 Let G be a connected graph. The subdivision graph S(G) of a graph (G) is the graph obtained by inserting a new vertex into every edge of G. The set of such new vertices is denoted by I(G).
Qun Liu
doaj +1 more source
Constraint interface preconditioning for topology optimization problems [PDF]
, 2015 The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity and size.
Kocvara, Michal +2 more
core +2 more sources
Structures preserved by generalized inversion and Schur complementation
Linear Algebra and its Applications, 2010 The authors investigate the inheritance of certain structures under generalized matrix inversion. These consist of rank and displacement structures. The study is done in such a way that the derivation of the preservation of rank structure can be carried over to that of the displacement structure.
Delvaux, Steven, Barel, Marc Van
openaire +2 more sources
, 2020 For both isothermal and thermal petroleum reservoir simulation, the Constrained Pressure Residual (CPR) method is the industry-standard preconditioner. This method is a two-stage process involving the solution of a restricted pressure system.
Jönsthövel, Tom B +3 more
core +1 more source
Linear Algebra and its Applications, 1979 AbstractLet A be an n×n complex matrix. For a suitable subspace M of Cn the Schur compression A M and the (generalized) Schur complement A/M are defined. If A is written in the form A= BCST according to the decomposition Cn=M⊕M⊥ and if B is invertible, then AM=BCSSB−1C and A/M=000T−SB−1C· The commutativity rule for Schur complements is proved: (A/M)/N=(
openaire +1 more source
A preconditioner for the Schur complement matrix [PDF]
, 2006 A preconditioner for iterative solution of the interface problem in Schur Complement Domain Decomposition Methods is presented. This preconditioner is based on solving a global problem in a narrow strip around the interface.
Dalcin, Lisandro Daniel +5 more
core +2 more sources