with the K 9 K matrix P (sometimes referred to as the Gram matrix) with elements P jk ¼ P l v jl v kl , the K 9 1 vector d with elements d k ¼ P l a l v kl , and the K 9 1 vector c representing the unknown distribution. The unique best-fit solution with the nonnegativity constraint c k C 0 can be found unambiguously with the algebraic algorithm NNLS, which was introduced and proven by Lawson and Hanson (1974) . We first used the NNLS algorithm in the context of SV distribution analysis, in a form where we expressed all requisite quantities with elements of the normal equations (Schuck 2000) . NNLS is an active set algorithm that divides the unknowns into sets with active (c k = 0) and inactive (c k [ 0) inequalities, and iteratively establishes the active set producing the best-fit solution. For the inactive set, the problem takes the same form as (5), but with all matrix and vector elements from components with active constraints deleted (Gill et al. 1986) .