Shape matrix decomposition is a subproblem in radiation therapy planning. A given fluence matrix A has to be written as a sum of shape matrices corresponding to homogeneous fields that can be shaped by a multileaf collimator. We solve the problem of finding an approximation B of A satisfying prescribed upper and lower bounds for each entry. The approximation B is determined such that the corresponding fluence can be realized with a prescribed delivery time using a multileaf collimator with an interleaf collision constraint, and under this condition the distance between A and B is minimized. © 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 57(2), 135–140 2011
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