Showing papers on "QR decomposition published in 1975"
TL;DR: The error analysis for computing the QR decomposition by Givens transformations was given originally by Wilkinson for n × n square matrices, and later by Gentleman for N × p (p ⩽ n ) tall thin matrices as mentioned in this paper.
80 citations
01 Jan 1975
TL;DR: Algorithms based on Powell's Hybrid Method and/or the Marquardt-Levenberg scheme for minimizing the sum of squares of nonlinear functions and requiring neither analytic nor numeric derivatives are considered.
Abstract: Algorithms based on Powell's Hybrid Method and/or the Marquardt-Levenberg scheme for minimizing the sum of squares of nonlinear functions and requiring neither analytic nor numeric derivatives are considered. These algorithms employ a pseudo-Jacobian matrix J which is updated by an unsymmetric rank-one formula at each cycle. Two factorizations, the QR factorization of J and the RTR factorization of JTJ, are studied, and implementational details concerned with the careful and efficient updating of these factorizations are presented. It is indicated how degeneracies may be monitored via the factorizations, and some observations are presented based upon test-code results.
1 citations