We describe a paradigm for numerical computing, based on exact computation. This emerging paradigm has many advantages compared to the standard paradigm which is based on fixed-precision. We first survey the literature on multiprecision number packages, a prerequisite for exact computation. Next we survey some recent applications of this paradigm. Finally, we outline some basic theory and techniques in this paradigm. 1 This paper will appear as a chapter in the 2nd edition of Computing in Euclidean Geometry, edited by D.-Z. Du and F.K. Hwang, published by World Scientific Press, 1994. 1 1 Two Numerical Computing Paradigms Computation has always been intimately associated with numbers: computability theory was early on formulated as a theory of computable numbers, the first computers have been number crunchers and the original mass-produced computers were pocket calculators. Although one's first exposure to computers today is likely to be some non-numerical application, numeri...

In this paper we review the current state of the problem solving environment (PSE) field and make projections for the future. First we describe the computing context, the definition of a PSE and the goals of a PSE. The state-of-the-art is summarized along with sources (books, bibliographics, web sites) of more detailed information. The principal components and paradigms for building PSEs are presented. The discussion of the future is given in three parts: future trends, scenarios for 2010/2025, and research

this article we describe our view of the area and relate it to the problem solving processes in science and engineering. Realities

In 1991, the US Congress passed the High Performance Computing and Communications bill, commonly known as the HPCC bill, enshrining the Grand Challenges as national priorities. The very nature of these problems require the multidisciplinary teamwork of engineers plus computer, mathematical and physical scientists. But many important scientific and engineering problems are solved daily on workstations---these were dubbed the "petty challenges". Both classes of problem are demanding computational systems although quite different from non-scientific systems. We review a philosophical background for CSE, using this development to point out how seemingly innocuous decisions made by engineers and scientists can have disastrous results. Hence, software engineers should see CSE as a professional challenge. Our program is based on studying applications, the algorithms to solve problems arising in those applications, and the mapping of those algorithms to architectures. Using Computing Reviews...

ion Bisection method Procedures Weightlifting kinematics Program structure Weightlifting kinematics Simple statements Rod stacking Functions Sliding block Conditionals Root finding While loops Numerical integration For loops Heat flow Arrays Curve fitting Array parameters Visualizing heat flow File input/output Table 1: Summary of revised lessons related course materials have observed the susceptibility of such material to "upward creep" in scope and difficulty. The typical revised lesson uses one motivating problem to illustrate one or two key computing or problem-solving concepts. The most complicated mathematics that we use in any of the lessons is simple integration. Each of our original lessons introduced several new concepts and used them to solve one or two representative problems. Even so, we decided that many of the lessons were not sufficiently centered around the problems. In retrospect, this is evident from the breakdown of the lessons listed previously: they are organized...

Abstract not found

s is typically a one- or two-year program in a field that is in some sense related to, but different from, the discipline chosen by the student in the first two cycles. Hence the third cycle is, in the current context, the only framework for the organization of interdisciplinary CS&E programs. Students interested in CS&E can currently choose from a small range of advanced programs such as Computer Science and Industrial Mathematics, Biomedical and Clinical Engineering, Biostatistics and so on. For the sake of completeness, we should mention that besides the university engineering degree, which is referred to as civil engineering degree, there is also an industrial engineering degree. The educational program for industrial engineers takes four years and is taught at non-university schools for higher education. However, in the sequel of the text we shall focus only on university curricula. May we remark that worldwide the Belgian educational system has a

This paper briefly introduces the field computational science and engineering (CS&E), and is an attempt to get other computer scientists more interested in CS&E related activities. It starts by giving a short outline of the increased international activity in the field. Several of the definitions of CS&E that have been given are presented, with an emphasis on how the field is related to computer science. The role of supercomputers is discussed, and we try to identify important challenges for future CS&E education and research, again with a hope to attract computer scientists.

Committee on Cyberinfrastructure, all opinions, findings, and recommendations expressed within it are those of the CLWD Task Force and do not necessarily reflect the views of