Results 11 to 20 of about 1,121,911 (166)
Perturbation Bound of the Group Inverse and the Generalized Schur Complement in Banach Algebra [PDF]
Abstract and Applied Analysis, 2012 We investigate the relative perturbation bound of the group inverse and also consider the perturbation bound of the generalized Schur complement in a Banach algebra.
Xiaoji Liu, Yonghui Qin, Hui Wei
doaj +5 more sources
Generalized Schur complements [PDF]
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=(
Ando, T.
openaire +2 more sources
Some inequalities on generalized Schur complements [PDF]
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 +2 more sources
Schur complement of general H‐matrices [PDF]
Numerical Linear Algebra with Applications, 2009 AbstractIt is well known that the Schur complement of some H‐matrices is an H‐matrix. In this paper, the Schur complement of any general H‐matrix is studied. In particular, it is proved that the Schur complement, if it exists, is an H‐matrix and the class to which the Schur complement belongs is studied.
Rafael Bru +3 more
openaire +6 more sources
Mendelianization: Concentrating Polygenic Signal Into a Single Causal Locus. [PDF]
Genet EpidemiolABSTRACT Complex disorders such as depression and alcohol use involve numerous genetic variants, and implicated loci continue to grow with sample size. This proliferation hampers interpretability, as the mechanisms by which so many variants jointly contribute to pathophysiology remain unclear.
Strobl EV.
europepmc +2 more sources
Six generalized Schur complements [PDF]
Linear Algebra and its Applications, 1988 The authors give a unified treatment of equivalence between some old and new generalizations of the Schur complement of matrices.
Butler, C.A., Morley, T.D.
openaire +3 more sources
The Schur complements of generalized doubly diagonally dominant matrices [PDF]
Linear Algebra and its Applications, 2004 It is known that the Schur complements of diagonally dominant matrices are diagonally dominant, and that the same is true for doubly diagonally dominant matrices. In this paper, the authors extend these results to the generalized doubly diagonally dominant matrices (a proper subset of H-matrices); that is, they show that the Schur complement of a ...
Liu, Jianzhou +2 more
openaire +4 more sources
Notes on the Schur-convexity of the Extended Mean Values [PDF]
, 2002 In this article, the Schur-convexities of the weighted arithmetic mean of function and the extended mean values are proved. Moreover, some inequalities involving the arithmetic mean, the harmonic mean, the logarithmic mean, and comparison between the ...
Qi, Feng +3 more
core +6 more sources
Schur-convexity of the Extended Mean Values [PDF]
, 2001 In this article, the Schur-convexity of the extended mean values are proved. Consequently, an inequality between the logarithmic mean values and the identity (exponential) mean values is ...
Qi, Feng
core +6 more sources
Idempotent operator and its applications in Schur complements on Hilbert C*-module
Special Matrices, 2023 The present study proves that TT is an idempotent operator if and only if R(I−T∗)⊕R(T)=X{\mathcal{ {\mathcal R} }}\left(I-{T}^{\ast })\oplus {\mathcal{ {\mathcal R} }}\left(T)={\mathcal{X}} and (T∗T)†=(T†)2T{\left({T}^{\ast }T)}^{\dagger }={\left({T ...
Karizaki Mehdi Mohammadzadeh +1 more
doaj +1 more source