On the Level-2 Condition Number for Moore–Penrose Inverse in Hilbert Space

Huaian Diao () and Yimin Wei ()
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Huaian Diao: Northeast Normal University, School of Mathematics and Statistics & Key Laboratory of Applied Statistics of MOE
Yimin Wei: Ministry of Education, Fudan University, School of Mathematical Science and Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University)

A chapter in Combinatorial Matrix Theory and Generalized Inverses of Matrices, 2013, pp 159-169 from Springer

Abstract: Abstract We prove that ${\rm{cond}}_{\dagger}(T)-1\leq {\rm{cond}}^{[2]}_{\dagger}(T)\leq{\rm{cond}}_{\dagger}(T)+1$ , where T is a linear operator in a Hilbert space, ${\rm{cond}}_{\dagger}(T)$ is the condition number of computing its Moore–Penrose inverse, and ${\rm{cond}}^{[2]}_{\dagger}(T)$ is the level-2 condition number of this problem.

Keywords: Condition number; Linear operator; Moore–Penrose inverse; Perturbation; 15A09; 15A60; 15A35 (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-1053-5_13

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DOI: 10.1007/978-81-322-1053-5_13

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