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We propose as an optimization technique singular value decomposition (SVD) analysis, which allows the measurement of ill conditioning of the stereotactic radiotherapy inverse problem and yields optimal weights for conformal treatment. Our approach to dose distribution optimization is to recover estimates of the minibeams weights from well\u2010defined previsional dose matrices to study the influence of the different parameters on the stereotactic radiotherapy inverse procedure. The adjustment of the different parameters of the stereotactic irradiation to the \u201cSVD optimizer\u201d procedure is realized taking into account the ratio of the quality reconstruction to the calculation time. It will permit a more efficient use of the SVD optimizer in clinical applications with real three\u2010dimensional lesions. We show the efficiency of the SVD optimizer in analyzing and predicting ill conditioning in stereotactic radiotherapy and in recognizing the topography of the different beams to create an optimal vector containing the beam weights (reconstructed weighting vector).<\/jats:p>","DOI":"10.1002\/ima.1850060113","type":"journal-article","created":{"date-parts":[[2007,3,5]],"date-time":"2007-03-05T23:08:36Z","timestamp":1173136116000},"page":"104-113","source":"Crossref","is-referenced-by-count":9,"title":["Study of the degree of III conditioning of the phase space of pencil\u2010beam radiotherapy using singular value decomposition"],"prefix":"10.1002","volume":"6","author":[{"given":"D.","family":"Lefkopoulos","sequence":"first","affiliation":[]},{"given":"P.","family":"Grandjean","sequence":"additional","affiliation":[]},{"given":"A.","family":"Laouar","sequence":"additional","affiliation":[]},{"given":"M.","family":"Schlienger","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2005,10,20]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"385","article-title":"Hyperselective encephalic irradiation with linear accelerator","volume":"33","author":"Betti O.","year":"1984","journal-title":"Acta Neurol."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/35\/10\/007"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8140(88)90167-3"},{"key":"e_1_2_1_5_2","volume-title":"Generalized Inverses of Linear Transformations","author":"Campbell S. 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