T. J. Dekker

Bio: T. J. Dekker is an academic researcher from University of Amsterdam. The author has contributed to research in topics: Numerical linear algebra & Gaussian elimination. The author has an hindex of 10, co-authored 20 publications receiving 754 citations.

A floating-point technique for extending the available precision

Abstract: A technique is described for expressing multilength floating-point arithmetic in terms of singlelength floating point arithmetic, i.e. the arithmetic for an available (say: single or double precision) floating-point number system. The basic algorithms are exact addition and multiplication of two singlelength floating-point numbers, delivering the result as a doublelength floating-point number. A straight-forward application of the technique yields a set of algorithms for doublelength arithmetic which are given as ALGOL 60 procedures.

Algorithms and applications on vector and parallel computers

Abstract: The gigantic capacities of present-day supercomputers, both with respect to computing power and to data storage, offer the possibility of tackling problems of a size and complexity which could not be handled before. The efficient use of these machines often requires the design of new numerical algorithms, or the re-design of existing algorithms and data organization in order to meet the possibilities of the new architectures. This development, in combination with the advent of two supercomputers in the Netherlands (a Cray-1 and a CDC Cuber 205) gave the impetus to the editors of this book to start a Colloquium on Numerical Aspects of Vector and Parallel Processors. In the majority of the papers one of the following vector and/or parallel computers plays a role: CDC Cyber 205, Cray-1, Cray X/MP, VP-200, DPP84.

Rehabilitation of the Gauss-Jordan algorithm

Abstract: In this paper a Gauss-Jordan algorithm with column interchanges is presented and analysed. We show that, in contrast with Gaussian elimination, the Gauss-Jordan algorithm has essentially differing properties when using column interchanges instead of row interchanges for improving the numerical stability. For solutions obtained by Gauss-Jordan with column interchanges, a more satisfactory bound for the residual norm can be given. The analysis gives theoretical evidence that the algorithm yields numerical solutions as good as those obtained by Gaussian elimination and that, in most practical situations, the residuals are equally small. This is confirmed by numerical experiments. Moreover, timing experiments on a Cyber 205 vector computer show that the algorithm presented has good vectorisation properties.

What every computer scientist should know about floating-point arithmetic

Abstract: Floating-point arithmetic is considered as esoteric subject by many people. This is rather surprising, because floating-point is ubiquitous in computer systems: Almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow. This paper presents a tutorial on the aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating point standard, and concludes with examples of how computer system builders can better support floating point.

The Tera computer system

Abstract: The Tera architecture was designed with several ma jor goals in mind. First, it needed to be suitable for very high speed implementations, i. e., admit a short clock period and be scalable to many processors. This goal will be achieved; a maximum configuration of the first implementation of the architecture will have 256 processors, 512 memory units, 256 I/O cache units, 256 I/O processors, and 4096 interconnection network nodes and a clock period less than 3 nanoseconds. The abstract architecture is scalable essentially without limit (although a particular implementation is not, of course). The only requirement is that the number of instruction streams increase more rapidly than the number of physical processors. Although this means that speedup is sublinear in the number of instruction streams, it can still increase linearly with the number of physical pro cessors. The price/performance ratio of the system is unmatched, and puts Tera’s high performance within economic reach. Second, it was important that the architecture be applicable to a wide spectrum of problems. Programs that do not vectoriae well, perhaps because of a preponderance of scalar operations or too-frequent conditional branches, will execute efficiently as long as there is sufficient parallelism to keep the processors busy. Virtually any parallelism available in the total computational workload can be turned into speed, from operation level parallelism within program basic blocks to multiuser timeand space-sharing. The architecture

Computational methods of linear algebra

Abstract: The authors' survey paper is devoted to the present state of computational methods in linear algebra. Questions discussed are the means and methods of estimating the quality of numerical solution of computational problems, the generalized inverse of a matrix, the solution of systems with rectangular and poorly conditioned matrices, the inverse eigenvalue problem, and more traditional questions such as algebraic eigenvalue problems and the solution of systems with a square matrix (by direct and iterative methods).

Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates,

Abstract: Exact computer arithmetic has a variety of uses, including the robust implementation of geometric algorithms. This article has three purposes. The first is to offer fast software-level algorithms for exact addition and multiplication of arbitrary precision floating-point values. The second is to propose a technique for adaptive precision arithmetic that can often speed these algorithms when they are used to perform multiprecision calculations that do not always require exact arithmetic, but must satisfy some error bound. The third is to use these techniques to develop implementations of several common geometric calculations whose required degree of accuracy depends on their inputs. These robust geometric predicates are adaptive; their running time depends on the degree of uncertainty of the result, and is usually small.

Density functional calculations of nuclear magnetic shieldings using the zeroth-order regular approximation (ZORA) for relativistic effects: ZORA nuclear magnetic resonance

Abstract: We present a new relativistic formulation for the calculation of nuclear magnetic resonance (NMR) shielding tensors. The formulation makes use of gauge-including atomic orbitals and is based on density functional theory. The relativistic effects are included by making use of the zeroth-order regular approximation. This formulation has been implemented and the 199Hg NMR shifts of HgMe2, HgMeCN, Hg(CN)2, HgMeCl, HgMeBr, HgMeI, HgCl2, HgBr2, and HgI2 have been calculated using both experimental and optimized geometries. For experimental geometries, good qualitative agreement with experiment is obtained. Quantitatively, the calculated results deviate from experiment on average by 163 ppm, which is approximately 3% of the range of 199Hg NMR. The experimental effects of an electron donating solvent on the mercury shifts have been reproduced with calculations on HgCl2(NH3)2, HgBr2(NH3)2, and HgI2(NH3)2. In addition, it is shown that the mercury NMR shieldings are sensitive to geometry with changes for HgCl2 of a...