AbstTuct A new methocl is proposed t,o solve systems of linear approximate equations Xe fu y where the unkllowns e ancl the data y are posit,ive and the matrix X coiisists of nonnegat,ive elemeiits. "'riting the i-th near-equality Xi.O!y,i Rt 1 the assumed model is Xi.efyi == <i with mutually indcpendent positive errors C, . The loss function is defined b.y EI) wiCCi -1) log Cle in whic:h w, is the importance weight for the i-th ncar-equality. A reparanieterization reduces the method to

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... ained minlmization ol' a smeoth strictly eonvex fLinction implying the unique existence of positive solution and the applicability of Newton7s method that converges quadratically. The solution stability is colltrolled by weighting prior' guesses of the unknowns e, The method matches thc maximum likelihood estiritation if all weights w,・ are eqllal ancl <i independently fbllow the probabiiity density function oc tW(i "), O < w .