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Structured least-squares problems and inverse eigenvalue problems for \((P,Q)\)-reflexive matrices. (English) Zbl 1336.65061

Summary: A new meaningful structured matrix – \((P,Q\))-reflexive matrix – is defined. Without the common assumption that \(P\) or \(Q\) is unitary, a general solution is derived for its structured least-squares problem. As a necessary and sufficient condition being presented for the solvability of its structured inverse eigenvalue problem, structured constrains are firstly given to guarantee the existence of the solution. The optimal approximation problem is also considered under spectral constrains.

MSC:

65F18 Numerical solutions to inverse eigenvalue problems
15A29 Inverse problems in linear algebra
65F20 Numerical solutions to overdetermined systems, pseudoinverses
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