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Dual algorithms for orthogonal Procrustes rotations. (English) Zbl 0664.65038

Let \(A_ 1,...,A_ m\) be given \(n\times k\)-matrices. The problem is to find orthogonal \(k\times k\)-matrices \(Y_ 1,...,Y_ m\) which maximize \(g(Y_ 1,...,Y_ m):=\sum_{i<j}tr(Y_ i^ TA_ i^ TA_ jY_ j).\) This problem is related to a minimization problem for an upper bound for g. Under an eigenvalue condition, this upper bound is sharp in the sense that its minimization yields a global maximizer of g. The upper bound is minimized via a regularized Newton-type algorithm. Problems are caused by points where the upper bound is not differentiable. The authors also report about the numerical performance of their algorithm in detail.
Reviewer: H.Engl

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
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