Active netlib: an active mathematical software collection for inquiry-based computational science & engineering education

A core subject in the undergraduate education of applicationscientists and engineers is the use of mathematical software tosolve computational problems. To make effective use of mathematicalsoftware, application developers need a basic understanding of theunderlying numerical methods and enough knowledge to be able tochoose an appropriate solver, parameterize it correctly, andvalidate the computed results. Correct results are of courserequired, but good computational performance is desired aswell. Most application scientists have neither the time nor theinterest to read the current literature in numerical analysis. Theysolve numerical problems by relying on the methods and programsthey learned about in previous coursework. This tendency has theunfortunate consequence that new methods with improvedfunctionality and/or efficiency may go unused by practicingengineers. Mathematical subroutine libraries can be highly complex.Few application scientists understand how they really work, and theusual practice is to treat the subroutines as "black boxes". Ablack box is a piece of software that can be used without knowledgeof its inner working; the user supplies the input, and the outputis more or less assumed to be correct. However, there are a numberof pitfalls in numerical computation (e.g., roundoff error,ill-conditioning, non-convergence). Application engineers needenough understanding of the underlying numerical methods to be ableto detect and diagnose problems that occur and to modify orcustomize the methods if necessary. This need is especially crucialin the use of iterative methods to solve large sparse linearsystems, where the problem may need to be properly preconditionedin order for convergence to occur and where the appropriate methodto employ depends on the nature of the problem being solved. A large amount of mathematical software is both commercially andfreely available. However, not all the software that is availableis of high quality. It can also be difficult to locate theappropriate software by using web search engines, since thedescriptions available for searching may be lacking or may notmatch the vocabulary used by the searcher. A good solution to theseproblems is to have experts in the field of numerical analysismaintain a moderated collection of high quality software which isorganized and cataloged with appropriate metadata to enable easysearching. The Netlib mathematical software repository is such a collectionthat has been contributed to and managed by the numerical analysiscommunity for the past fifteen years. To address the aforementioned problems, Active Netlib providesan active collection of high-quality mathematical softwareresources in the context of an inquiry-based learning environmentfor computational science and engineering education. The Netlibcollection is being extended in a number of ways to support thegoals of this project. The NetSolve client-server system foraccessing hardware and software resources over a network providesan active interface to the contents of Netlib. By making thesubroutines housed in Netlib available over the network oncomputational servers, NetSolve enables access to up-to-datemathematical software from a variety of client interfaces runningon users' workstations, without requiring the users to download andinstall the software themselves. Use of NetSolve seamlesslymaintains the currency and usability of the content as theunderlying hardware, operating systems, and software evolve.Furthermore, the NetSolve adaptive solver interface guides the userin selecting appropriate software, in setting parameters correctly,and in interpreting numerical results. The Netlib collection is being further extended through use ofthe Repository in a Box (RIB) toolkit, which enables an individualor organization to set up and maintain a repository that interactswith other RIB repositories. RIB will allow the Netlib collectionto be selectively mirrored and contributed to by all projectparticipants. In summary, the goals of the Active Netlib project are thefollowing: Remote executable content with highly interactive userinterfacesResource users becoming resource providersA growing network of software repositories and computationalservices drawn upon and contributed to by researchers, educators,and students.For more information, see the Active-Netlib home page athttp://icl.cs.utk.edu/active-netlib/.