Later Work on the Method of Situation

Abstract

The problem of choosing values for the unknowns x,y, z,etc to minimise the unconstrained sum of the absolute errors in the n linear equations

$$ {a_i}x + {b_i}y + {c_i}z + etc - {l_i} = 0,{\text{ i = 1,2,}} \ldots {\text{,n}} $$

had been proposed by Gauss in 1809 and named the Method of Situation by Laplace in 1818. Although Gauss had characterised the solution of this problem in a form which could have been developed as a simple algorithm, no further work on the unconstrained problem seems to have been published between 1818 and 1887, with the exception of the single sentence in the paper by Fourier (1824) noted in Chapter 4.