A new version of a preconditioning method for certain two-by-two block matrices with square blocks
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DOI: 10.1007/s10543-018-0741-x
Abstract: Two-by-two block matrices with square matrix blocks arise in many important applications. Since the problems are of large scale, iterative solution methods must be used. Thereby the choice of an efficient and robust preconditioner is… read more here.
Keywords: two two; new version; two block; block matrices ... See more keywords
The Drazin inverse of anti-triangular block matrices
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DOI: 10.1007/s12190-021-01638-2
Abstract: The aim of this paper is to establish formulae for the Drazin inverse of anti-triangular block matrices under new assumptions in literature. Precisely, we consider the Drazin inverse of three kinds of anti-triangular block matrices.… read more here.
Keywords: anti triangular; drazin inverse; block; triangular block ... See more keywords
Positive semi-definite 2 × 2 block matrices and norm inequalities
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DOI: 10.1016/j.laa.2018.03.046
Abstract: Abstract Let M = [ A X X ⁎ B ] ∈ C 2 n × 2 n be positive semi-definite 2 × 2 block matrix, where A , B , X ∈ C n… read more here.
Keywords: semi definite; positive semi; definite block; norm ... See more keywords
Representations for the image-kernel (p,q)-inverses of block matrices in rings
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DOI: 10.1515/gmj-2018-0042
Abstract: Abstract We present the conditions for a block matrix of a ring to have the image-kernel ( p , q ) {(p,q)} -inverse in the generalized Banachiewicz–Schur form. We give representations for the image-kernel inverses… read more here.
Keywords: image; image kernel; representations image; kernel inverses ... See more keywords
Generalizations of numerical radius inequalities related to block matrices
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DOI: 10.2298/fil1915981b
Abstract: We establish several numerical radius inequalities related to 2x2 positive semidefinite block matrices. It is shown that if A,B,C ? Mn(C) are such that [A B* B C] ? 0, then wr(B)? 1/2 ||Ar +… read more here.
Keywords: block matrices; inequalities related; numerical radius; radius inequalities ... See more keywords
A note on the Moore-Penrose inverse of block matrices
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DOI: 10.2298/fil2301173s
Abstract: Motivated by the representation for the Moore-Penrose inverse of the block matrix over a *-regular ring presented in [R.E. Hartwig and P. Patr?cio, When does the Moore-Penrose inverse flip? Operators and Matrices, 6(1):181-192, 2012], we… read more here.
Keywords: note moore; moore penrose; block matrices; penrose inverse ... See more keywords
An eigenvalue inequality for positive semidefinite k × k block matrices
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DOI: 10.7153/jmi-2020-14-90
Abstract: In this paper, we give some generalized results on matrix eigenvalue majorization inequality for positive semidefinite block matrices under a condition, which is a natural extended result given by Lin [4]. read more here.
Keywords: block matrices; inequality positive; positive semidefinite; semidefinite block ... See more keywords