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On Positive Semidefinite Preserving Stein Transformation
- Authors
- 송윤정
- Issue Date
- Jan-2015
- Publisher
- 한국전산응용수학회
- Keywords
- Stein Transformation; Semidefinite Linear Complementarity Problems (SDLCP); ${; bf P_2}$-property; ${; bf P_2' }$-property; strictly monotone; nondegenerate; ${; bf GUS}$-property.
- Citation
- Journal of Applied Mathematics and Informatics, v.33, no.1, pp.229 - 234
- Journal Title
- Journal of Applied Mathematics and Informatics
- Volume
- 33
- Number
- 1
- Start Page
- 229
- End Page
- 234
- ISSN
- 1598-5857
- Abstract
- In the setting of semidefinite linear complementarity problems on $\sn$,we focus on the Stein Transformation $S_A(X):= X - AXA^T$ for $A\in \Rnn$ that is positive semidefinite preserving (i.e., $S_A(\sn_+) \subseteq \sn_+$) and show that such transformation is strictly monotone if and only if it is nondegenerate. We also show that a positive semidefinite preserving $S_A$ has the Ultra-GUS property if and only if $1 \not\in \sigma(A)\sigma(A).$
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Related Researcher
- Song, Yoon Jung
- College of Natural Sciences (Department of Mathematics)