article Free AccessArtifacts AvailableArtifacts Evaluated & Reusable Share on Algorithm 686: FORTRAN subroutines for updating the QR decomposition Authors: L. Reichel Univ. of Kentucky, Lexington Univ. of Kentucky, LexingtonView Profile , W. B. Gragg Naval Postgraduate School, Monterey, CA Naval Postgraduate School, Monterey, CAView Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 16Issue 4Dec. 1990 pp 369–377https://doi.org/10.1145/98267.98291Published:01 December 1990Publication History 28citation1,592DownloadsMetricsTotal Citations28Total Downloads1,592Last 12 Months40Last 6 weeks6 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 Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

The order p which is obtainable with a stable k -step method in the numerical solution of y′ = f ( x , y ) is limited to p = k + 1 by the theorems of Dahlquist. In the present paper the customary schemes are modified by including the value of the derivative at one “nonstep point;” as usual, this value is gained from an explicit predictor. It is shown that the order of these generalized predictor-corrector methods is not subject to the above restrictions; stable k -step schemes with p = 2 k + 2 have been constructed for k ≤ 4. Furthermore it is proved that methods of order p actually converge like h p uniformly in a given interval of integration. Numerical examples give some first evidence of the power of the new methods.