The Fortran output routine messy enables debugging and error message processing strategies in the design of numerical and mathematical software. It supports separate output from different processes in a parallel computing environment.

A code is presented which offers a simple clean way to get output that is very easy to read. Special support is given for the output of error messages which are a part of an application package or subprogram library. The code uses many of the features in Fortran 2003, and the “NEWUNIT=” in an open statement from Fortran 2008. The latter can easily be replaced with “UNIT=99”. One goal here is to illustrate some of the nice features in recent incarnations of Fortran.

This note offers a new approach based on a least squares fit to past data in order to select the stepsize when solving an ordinary differential equation. The approach used may have applicability to other situations where one wants to repeatedly make short term predictions given somewhat noisy data. Additional ad hoc rules help significantly for reliability and efficiency. Comparisons with some Runge-Kutta codes, an Adams code, and an extrapolation code are also included.

A new algorithm is presented for solving nonlinear least-squares and nonlinear equation problems. The algorithm is based on approximating the nonlinear functions using the quadratic-tensor model proposed by Schnabel and Frank. The problem statement may include simple bounds or more general linear constraints on the unknowns. The algorithm uses a trust-region defined by a box containing the current values of the unknowns. The objective function (Euclidean length of the functions) is allowed to increase at intermediate steps. These increases are allowed as long as our predictor indicates that a new set of best values exists in the trust-region. There is logic provided to retreat to the current best values, should that be required. The computations for the model-problem require a constrained nonlinear least-squares solver. This is done using a simpler version of the algorithm. In its present form the algorithm is effective for problems with linear constraints and dense Jacobian matrices. Results on standard test problems are presented in the Appendix. The new algorithm appears to be efficient in terms of function and Jacobian evaluations.

article Free Access Share on ACM Algorithms Policy Author: Fred T. Krogh View Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 17Issue 3pp 427–430https://doi.org/10.1145/114697.356357Published:01 September 1991Publication History 1citation198DownloadsMetricsTotal Citations1Total Downloads198Last 12 Months8Last 6 weeks4 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 method is presented to reduce the number of coefficients necessary to represent Patterson's quadrature formulae, to reduce the amount of storage necessary for storing function values, and to produce slightly smaller error in evaluating the formulae.

article ACM Algorithms Policy Share on Author: Fred T. Krogh View Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 15Issue 2June 1989 pp 169–172https://doi.org/10.1145/63522.356273Online:01 June 1989Publication History 0citation187DownloadsMetricsTotal Citations0Total Downloads187Last 12 Months1Last 6 weeks0 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 SiteGet Access

A contribution should be in the form of an algorithm, comparison, certification, remark, or translation.Algorithms ACM Algorithms are published to make the fruits of software research readily available to as wide an audience as possible.An algorithm must either provide a capability not readily available or perform a task better in some way than has been done before."Better" can mean anything from improved reliability or efficiency to more attractive packaging.In all cases, an algorithm must be of lasting value and must represent a substantial contribution in terms of the amount of work or the originality required for its creation.In most cases the communication of new algorithmic ideas should be done either in a companion paper published in one of the ACM Transactions or in previously published work.The textual part of an algorithm submission should give a brief description of what the algorithm does and pertinent information on usage and maintenance.It should not duplicate information in another paper or in the algorithm listing.It is recognized that certain algorithms will be useful to readers of one of the ACM Transactions but deal with subjects not in the usual research domain of that journal.When appropriate, the Algorithms Editor will guide authors to other ACM journals for possible publication of such algorithms.An ACM algorithm must be complete, portable, well documented, and well structured.The meaning of these terms is clarified below.

article Artifacts Evaluated & ReusableArtifacts AvailableAlgorithm 653: Translation of algorithm 539: PC-BLAS, basic linear algebra subprograms for FORTRAN usage with the INTEL 8087, 80287 numeric data processor Authors: R. J. Hanson ADI Corp., Sandia National Laboratories, 3800 Stone School Road, Ann Arbor, MI ADI Corp., Sandia National Laboratories, 3800 Stone School Road, Ann Arbor, MIView Profile , F. T. Krogh Applied Mathematics Group, Jet Propulsion Laboratory, Pasadena, CA Applied Mathematics Group, Jet Propulsion Laboratory, Pasadena, CAView Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 13Issue 3pp 311–317https://doi.org/10.1145/29380.214346Published:01 September 1987Publication History 7citation465DownloadsMetricsTotal Citations7Total Downloads465Last 12 Months35Last 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 contribution should be in the form of an algorithm, comparison, certification, remark, or translation.Algorithms ACM Algorithms are published to make the fruits of software research readily available to as wide an audience as possible.An algorithm must either provide a capability not readily available or perform a task better in some way than has been done before."Better" can mean anything from improved reliability or efficiency to more attractive packaging.In all cases, an algorithm must be of lasting value and must represent a substantial contribution in terms of the amount of work or the originality required for its creation.In most cases the communication of new algorithmic ideas should be done either in a companion paper published in one of the ACM Transactions or in previously published work.The textual part of an algorithm submission should give a brief description of what the algorithm does and pertinent information on usage and maintenance.It should not duplicate information in another paper or in the algorithm listing.It is recognized that certain algorithms will be useful to readers of one of the ACM Transactions but deal with subjects not in the usual research domain of that journal.When appropriate, the Algorithms Editor will guide authors to other ACM journals for possible publication of such algorithms.An ACM algorithm must be complete, portable, well documented, and well structured.The meaning of these terms is clarified below.

article ACM Algorithms Policy Share on Author: Fred T. Krogh View Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 12Issue 2June 1986 pp 171–174https://doi.org/10.1145/6497.356171Online:01 June 1986Publication History 1citation132DownloadsMetricsTotal Citations1Total Downloads132Last 12 Months1Last 6 weeks0 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 SiteGet Access

article Free Access Share on ACM Algorithms Policy Author: Fred T. Krogh View Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 11Issue 2June 1985 pp 193–196https://doi.org/10.1145/214392.356134Published:01 June 1985Publication History 0citation137DownloadsMetricsTotal Citations0Total Downloads137Last 12 Months3Last 6 weeks1 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

ACM Algorithms are published to make the fruits of software research readily available to as wide an audience as possible.An algorithm must either provide a capability not readily available or perform a task better in some way than has been done before."Better" can mean anything from improved reliability or efficiency to more attractive packaging.In all cases, an algorithm must be of lasting value and must represent a substantial contribution in terms of the amount of work or the originality required for its creation.In most cases the communication of new algorithmic ideas should be done either in a companion paper published in one of the ACM Transactions or in previously published work.The textual part of an algorithm submission should give a brief description of what the algorithm does and pertinent information on usage and maintenance.It should not duplicate information in another paper or in the algorithm listing.It is recognized that certain algorithms will be useful to readers of one of the ACM Transactions but deal with subjects not in the usual research domain of that journal.When appropriate, the Algorithms Editor will guide authors to other ACM journals for possible publication of such algorithms.An ACM algorithm must be complete, portable, well documented, and well structured.The meaning of these terms is clarified below.

Methods based on backward differentiation formulas (BDFs) for solving stiff differential equations require iterating to approximate the solution of the corrector equation on each step.One hope for reducing the cost of this is to make do w~th iteration matrices that are known to have errors and to do no more iterations than are necessary to maintain the stability of the method.This paper, following work by Klopfenstem, examines the effect of errors m the iteration matrix on the stability of the method.Apphcation of the results to an algorithm is discussed briefly.

A contribution should be in the form of an algorithm, comparison, certification, remark, or translation.Algorithms ACM Algorithms are published to make the fruits of software research readily available to as wide an audience as possible.An algorithm must either provide a capability not readily available or perform a task better in some way than has been done before."Better" can mean anything from improved reliability or efficiency to more attractive packaging.In all cases, an algorithm must be of lasting value and must represent a substantial contribution in terms of the amount of work or the originality required for its creation.In most cases the communication of new algorithmic ideas should be done either in a companion paper published in one of the ACM Transactions or in previously published work.The textual part of an algorithm submission should give a brief description of what the algorithm does and pertinent information on usage and maintenance.It should not duplicate information in another paper or in the algorithm listing.It is recognized that certain algorithms will be useful to readers of one of the ACM Transactions but deal with subjects not in the usual research domain of that journal.When appropriate, the Algorithms Editor will guide authors to other ACM journals for possible publication of such algorithms.An ACM algorithm must be complete, portable, well documented, and well structured.The meaning of these terms is clarified below.i T h e P F O R T verifier checks a F O R T R A N program for conformance with a portable subset of the former ANSI X3.9-1966 F O R T R A N standard.

ACM Algorithms are published to make the fruits of software research readily available to as wide an audience as possible.An algorithm must either provide a capability not readily available or perform a task better in some way than has been done before."Better" can mean anything from improved reliability or efficiency to more attractive packaging.In all cases, an algorithm must be of lasting value and must represent a substantial contribution in terms of the amount of work or the originality required for its creation.In most cases the communication of new algorithmic ideas should be done either in a companion paper published in one of the ACM Transactions or in previously published work.The textual part of an algorithm submission should give a brief description of what the algorithm does and pertinent information on usage and maintenance.It should not duplicate information in another paper or in the algorithm listing.It is recognized that certain algorithms will be useful to readers of one of the ACM Transactions but deal with subjects not in the usual research domain of that journal.When appropriate, the Algorithms Editor will guide authors to other ACM journals for possible publication of such algorithms.An ACM algorithm must be complete, portable, well documented, and well structured.The meaning of these terms is clarified below.1. Completeness: With the exception of code used from a previously published

ACM Algorithms are published to make the fruits of software research readily available to as wide an audience as possible.An algorithm must either provide a capability not readily available or perform a task better in some way than has been done before."Better" can mean anything from improved reliability or efficiency to more attractive packaging.In all cases, an algorithm must be of lasting value and must represent a substantial contribution in terms of the amount of work or the originality required for its creation.In most cases the communication of new algorithmic ideas should be done either in a companion paper published in one of the ACM Transactions or in previously published work.The textual part of an algorithm submission should give a brief description of what the algorithm does and pertinent information on usage and maintenance.It should not duplicate information in another paper or in the algorithm listing.Algorithms which serve only a very narrow application area will be considered only if they require less than a single printed page and if complete documentation is available in other published work or in machine readable form with the algorithm submission.An ACM algorithm must be complete, portable, well documented, and well structured.The meaning of these terms is clarified below.

A package of 38 low level subprograms for many of the basic operations of numerical linear algebra m presented.The package is intended to be used with Fortran.The operations m the package include dot product, elementary vector operation, Givens transformation, vector copy and swap, vector norm, vector scaling, and the determination of the index of the vector component of largest magnitude.The subprograms and a test driver are avadable in portable Fortran.Versions of the subprograms are also provided in assembly language for the IBM 360/67, the CDC 6600 and CDC 7600, and the Univac 1108.

No abstract available.

article Free Access Share on Algorithms Policy Author: Fred T. Krogh View Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 4Issue 2June 1978 pp 97–99https://doi.org/10.1145/355780.355781Published:01 June 1978Publication History 2citation137DownloadsMetricsTotal Citations2Total Downloads137Last 12 Months3Last 6 weeks1 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

This paper discusses how to numerically test a subroutine for the solution of ordinary differential equations.Results obtained with a variable order Adams method are given for eleven simple test cases.

A procedure is described to test the individual components of the numerical solution to a system of differential equations for relative instability. Although the test is based on the theory for linear differential equations, it has also worked for nonlinear problems. Extra computation is negligible; the test involves checking the signs of previously computed numbers

Some new predictors are presented for use with the Adams-Moulton correctors of orders 4 through 8. The resulting algorithms have better stability characteristics than the usual ones which employ the Adams Bashforth predictors and at the same time require no additional storage. The regions of absolute and relative stability for the methods mentioned above and for the iterated Adams-Moulton correctors are given. Results obtained using the various methods are compared.