This paper is addressed to the classical problem of
estimating factor loadings under the condition that the sum
of squares of off-diagonal residuals be minimized.
Communalities consistent with this criterion are produced
as a by-product. The experimental work included several
alternative algorithms before a highly efficient method was
developed. The final procedure is illustrated with a
numerical example. Some relationships of minres to
principal-factor analysis and maximum-likelihood factor
estimates are discussed, and several unresolved problems
are pointed out.