A computerized intensity modulated radiotherapy (IMRT) dosage optimization comprises: dividing the volume into dose voxels (102) to be irradiated with weighted pencil beams from gantry angles; selecting dose voxels (104) from the planning target volume (PTV), organs at risk (OAR) and normal tissue in the PTV neighborhood; choosing a dose matrix (106) for the voxels; constructing beam weight vectors (108); calculating a transfer matrix (110); inverting the matrix (112); populating the beam weight vector with the product of the inverted transfer matrix and the dose matrix (114); iteratively modifying dose values (118); and repeating the matrix multiplication (114) until negative beam weights are eliminated (116).
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