No abstract available.

A software package based on a modification of the Weeks' method is presented for calculating function values f ( t ) of the inverse Laplace transform. This method requires transform values F ( z ) at arbitrary points in the complex plane, and is suitable when f ( t ) has continuous derivatives of all orders; it is especially attractive when f ( t ) is required at a number of different abscissas t .

article Free AccessArtifacts Evaluated & ReusableArtifacts AvailableAlgorithm 662: A Fortran software package for the numerical inversion of the Laplace transform based on Weeks' method Authors: B. S. Garbow Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, ILView Profile , G. Giunta Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, ILView Profile , J. N. Lyness Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, ILView Profile , A. Murli Dipartimento di Matematica e Applicazioni, Universitá di Napoli, Via Mezzocannone 8, 80134 Napoli, Italy Dipartimento di Matematica e Applicazioni, Universitá di Napoli, Via Mezzocannone 8, 80134 Napoli, ItalyView Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 14Issue 2June 1988 pp 171–176https://doi.org/10.1145/45054.214375Published:01 June 1988Publication History 22citation1,248DownloadsMetricsTotal Citations22Total Downloads1,248Last 12 Months26Last 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

No abstract available.

A software interface problem occurs when two or more Items of software are used in conjunction with one another If proper advantage of using good software is to be gained, the user has to connect them properly.In this paper the problem of double integration employmg two similar one-dimensional adaptive quadrature routines is considered.If an absolute error no greater than eT in the final result is desired, it is necessary to determine what tolerance parameter ~o to assign to the outer routine and what tolerance parameters ~z, to assign for calls to the inner routine.Since it is not known at the outset how many times the inner routine will be called, there is reqmred what is termed an accuracyasstgnment strategy for determining ez,.In this paper two simple accuracy assignment strategms are discussed m detail.It ~s shown that one of them can be unstable if the outer routine is constructed internally in one way (local error control), but that it is quite 5cable ff it is constructed in another way (global error control).It is also found that one of the strategms is margmally more efficmnt for visually smooth integrands, while the other is significantly more efficient for peaked integrands Key Words and Phrases.adaptive integration, double integratmn, quadrature, automatm quadrature routine, software interface CR Categories: 5 16 1, INTRODUCTORY REMARKS ON THE SOFTWARE INTERFACE PROBLEMThis paper is about a single numerical software interface problem.Such problems are simple to state.In this case we plan to use two adaptive quadrature routines back to back for a double integration.The only nontrivial question is that of setting the two tolerance parameters involved so as to obtain a specified overall tolerance.This paper is devoted to examining only two possible strategies for this, one of which is obvious, in a context where only one type of automatic This work was performed under the auspices of the U.S.

The present unconstrained proliferation of automatic quadrature routines is a phenomenon which is wasteful in human time and computing resources. At the root of the problem in an absence of generally acceptable standards or benchmarks for comparing or evaluating such routines. In this paper we describe a general technique, based on the nature of the performance profile, which can be used for evaluation of routines.

General properties of automatic quadrature routines are described, and the conflict between reliablhty and economy whmh arises when one constructs such a routine is discussed m detail.The concept of the "performance profile" is introduced; this serves as an aid m understanding how such routines may fail for some problems and why the cost IS so much higher than in a nonautomatic routine.The relationship (often tenuous) between analytic results from numerical analysis relating to quadrature rules and the actual strategy used in these routines is discussed.Attention is drawn to the fact that an automatm quadrature routine is based on an unrehable exact arithmetic algorithm and, unlike simpler routines, is not based on a finite decision process.In this paper, those aspects of automatm quadrature routines which are relevant in the context of testing routines are gathered together as an introduction to forthcoming specific testing techmques.

The possibility of round off or other statistical error in function values is sometimes not taken into account in the construction of automatic routines. The possible consequences of such an omission are discussed.

nsTm~c'r.The adaptive Simpson quadrature routine is described, and the properties of the approximation error are investigated on an elementary level.Even this superficial investigation iildieates some changes which might, improve the efficiency of th.e routine.Four specific moditications in the routine are suggested to implement these changes.

A method of numerical integration is described which uses a low order integration rule to obtain a high order result. The error is successively reduced, using a method based on the idea of Richardson's deferred approach to the limit. The method is restricted to hypercubic domains.

We investigate a selection of integration rules based on the combination of third degree rules for elementary three-dimensional sub-domains. The practical problems associated with the application of these rules to domains bounded by planes of a certain type are discussed in detail. These included integration rules for less symmetrical domains which may occur near the boundary of the volume of integration, methods for combining integration coefficients from adjacent sub-domains, and methods for changing net size within the volume of integration. Particular attention is paid to minimizing the number of points at which the function has to be evaluated, and error estimates in terms of computation time are given. A list of integration coefficients of general interest for three-dimensional integrations is presented. The discussion is generalized to n dimensions for hyper-cubic domains.