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Register a new userLeast-Squares Approximation by Elements from Matrix Orbits Achieved by Gradient Flows on Compact Lie Groups
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Thomas Schulte-Herbr\\\"uggen
Publication date
2008
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English
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Let $S(A)$ denote the orbit of a complex or real matrix $A$ under a certain equivalence relation such as unitary similarity, unitary equivalence, unitary congruences etc. Efficient gradient-flow algorithms are constructed to determine the best approximation of a given matrix $A_0$ by the sum of matrices in $S(A_1), ..., S(A_N)$ in the sense of finding the Euclidean least-squares distance $$min {|X_1+ ... + X_N - A_0|: X_j in S(A_j), j = 1, >..., N}.$$ Connections of the results to different pure and applied areas are discussed.
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