Variable projection for affinely structured low-rank approximation in weighted 2-norm
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Abstract
The structured low-rank approximation problem for general affine structures, weighted 2-norm and fixed elements is considered. The variable projection principle is used to reduce the dimensionality of the optimization problem. Algorithms for evaluation of the cost function, the gradient and approximation of the Hessian are developed. For $m \times n$ mosaic Hankel matrices the algorithms have complexity $O(m^2 n)$.
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