A method in a computer for optimizing a dosage of intensity modulated radiotherapy (IMRT) comprises the steps of: dividing a three dimensional (3D) volume into a grid of dose voxels, wherein each dose voxel receives a dose of radiation from at least one pencil beam having a pencil beam weight and a gantry angle; selecting a first set of dose voxels from the 3D volume positioned within at least one of a planning target volume (PTV), organs at risk (OAR), and normal tissue in a neighborhood of the PTV; choosing a dose matrix from the first set of dose voxels; constructing a beam weight vector of individual beam weights for each pencil beam at each gantry angle; calculating a transfer matrix representing a dose deposition to the dose voxels from each pencil beam with unit beam weight; inverting the transfer matrix; performing a matrix multiplication of the inverted transfer matrix and the dose matrix and populating the beam weight vector with the results of the matrix multiplication; and iteratively modifying a plurality of doses in the dose matrix within a given range, wherein the range has a specific probability distribution function of acceptable dose values, and repeating the matrix multiplication until the negative weights in the beam weight vector are substantially eliminated, resulting in an optimized set of doses.
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