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期刊名称: Applications of Mathematics
Volume:64    Issue:2        Page:103-128
ISSN:0862-7940

Solvability classes for core problems in matrix total least squares minimization期刊论文

作者: Hnětynková Iveta Plešinger Martin Žáková Jana
DOI:10.21136/AM.2019.0252-18

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页码: 103-128
被引频次: 0
出版者: Springer Berlin Heidelberg,ACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS,Springer
期刊名称: Applications of Mathematics
ISSN: 0862-7940
卷期: Volume:64    Issue:2
语言: English
摘要: Linear matrix approximation problems AX ≈ B are often solved by the total least squares minimization (TLS). Unfortunately, the TLS solution may not exist in general. The so-called core problem theory brought an insight into this effect. Moreover, it simplified the solvability analysis if B is of column rank one by extracting a core problem having always a unique TLS solution. However, if the rank of B is larger, the core problem may stay unsolvable in the TLS sense, as shown for the first time by Hnětynková, Plešinger, and Sima (2016). Full classification of core problems with respect to their solvability is still missing. Here we fill this gap. Then we concentrate on the so-called composed (or reducible) core problems that can be represented by a composition of several smaller core problems. We analyze how the solvability class of the components influences the solvability class of the composed problem. We also show on an example that the TLS solvability class of a core problem may be in some sense improved by its composition with a suitably chosen component. The existence of irreducible problems in various solvability classes is discussed.
相关主题: total least squares, Theoretical, Mathematical and Computational Physics, 15A06, Mathematics, classification, 15A09, Optimization, 15A18, core problem theory, (ir)reducible problem, 15A23, Classical and Continuum Physics, Analysis, Mathematical and Computational Engineering, 65F20, Applications of Mathematics, linear approximation problem, MATHEMATICS, APPLIED, Matrices, Research, Mathematical research, Least squares,

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