article Free Access Share on Exploratory Data Analysis in a Study of the Performance of Nonlinear Optimization Routines Authors: David C. Hoaglin Department of Statistics, Harvard University, Cambridge, MA Department of Statistics, Harvard University, Cambridge, MAView Profile , Virginia Klema Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MAView Profile , Stephen C. Peters Department of Statistics, Stanford University, Stanford, CA Department of Statistics, Stanford University, Stanford, CAView Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 8Issue 2pp 145–162https://doi.org/10.1145/355993.355996Published:01 June 1982Publication History 8citation406DownloadsMetricsTotal Citations8Total Downloads406Last 12 Months21Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

A description of a system of subroutines to compute solutions to the iteratively reweighted least squares problem is presented. The weights are determined from the data and linear fit and are computed as functions of the scaled residuals. Iteratively reweighted least squares is a part of robust statistics where robustness means relative insensitivity to moderate departures from assumptions. The software for iteratively reweighted least squares is cast as semi-portable Fortran code whose performance is unaffected (in the sense that performance will not be degraded) by the computer or operating-system environment in which it is used. An [ell sub1] start and an [ell sub2] start are provided. Eight weight functions, a numerical rank determination, convergence criterion, and a stem-and-leaf display are included.

We describe an algorithm that can be used to select a set of independent columns of a matrix when numerical rank can be determined, and we associate the uncertainty of the data with rank selection. Mathematical software written in Fortran which implements this algorithm is available for a variety of computing machines.