An algorithmic approach to orthogonal projections and moore-penrose inverses

Boulmaarouf, Z.; Miranda, Mercedes; Labrousse, J-Ph.

doi:10.1080/01630569708816746

Cited by 5 publications

(1 citation statement)

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“…We obtain as applications several results due to S. Maeda [16,18] or Z. Boulmaarouf, M. Fernandez Miranda and J.-Ph. Labrouse [4]. We also extend the theorem of T. Kato [11,Theorem 6.35] which states that the gap between two idempotents is bigger than the gap between the corresponding range projections.…”

Section: Introductionsupporting

confidence: 48%

On the Generalized Derivation Induced by Two Projections

Popovici

Sebestyén

2009

Integr. equ. oper. theory

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We prove thatwhere P and Q are orthogonal projections on Hilbert spaces H , resp. K and X is a bounded linear operator between K and H , generalizing the well-known Akhiezer-Glazman equality (the case K = H and X = 1 H ). Specializing, we obtain results by Z. Boulmaarouf, M. Fernandez Miranda and J.-Ph. Labrouse, T. Kato or S. Maeda. We extend a theorem of Y. Kato and give some sufficient conditions for the equality P X(1 − Q) = (1 − P )XQ . We generalize results by D. Buckholtz, J.J. Koliha and V. Rakočević or S. Maeda and provide several necessary and/or sufficient conditions for the (left, right) invertibility of P X − XQ. Certain counter-examples show the consistency of the theory. Mathematics Subject Classification (2000). Primary 47A05; Secondary 47A30, 46C05, 46C07.

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Section: Introductionsupporting

confidence: 48%

On the Generalized Derivation Induced by Two Projections

Popovici

Sebestyén

2009

Integr. equ. oper. theory

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Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra

Makai

Zemánek

2016

Czech Math J

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Generalizing earlier results about the set of idempotents in a Banach algebra, or of self-adjoint idempotents in a C * -algebra, we announce constructions of nice connecting paths in the connected components of the set of elements in a Banach algebra, or of self-adjoint elements in a C * -algebra, that satisfy a given polynomial equation, without multiple roots. In particular, we will prove that in the Banach algebra case every such non-central element lies on a complex line, all of whose points satisfy the given equation. We also formulate open questions.

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A Novel Iterative Method for Computing Generalized Inverse

2014

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In this letter, we propose a novel iterative method for computing generalized inverse, based on a novel KKT formulation. The proposed iterative algorithm requires making four matrix and vector multiplications at each iteration and thus has low computational complexity. The proposed method is proved to be globally convergent without any condition. Furthermore, for fast computing generalized inverse, we present an acceleration scheme based on the proposed iterative method. The global convergence of the proposed acceleration algorithm is also proved. Finally, the effectiveness of the proposed iterative algorithm is evaluated numerically.

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An algorithmic approach to orthogonal projections and moore-penrose inverses

Cited by 5 publications

References 0 publications

On the Generalized Derivation Induced by Two Projections

On the Generalized Derivation Induced by Two Projections

Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra

A Novel Iterative Method for Computing Generalized Inverse

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