A New Approach to Scientific Computation by Ulrich W. Kulisch, Willard L. Miranker

By Ulrich W. Kulisch, Willard L. Miranker

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Numerisches Rechnen wie es ist und wie es sein konnte, Jahrbuch Uberblicke Mathematik. Bibliographisches Institut. Lortz, B. (1971). Eine Langzahlarithmetik mit optimaler einseitiger Rundung, Dissertation, Universitat Karlsruhe. Moore, R. E. (1966). "Interval Analysis". Prentice Hall, Englewood Cliffs, New Jersey. Reinsch, Ch. (1979). Die Behandlung von Rundungsfehlern in der Numerischen Analysis, Jahrbuch Uberblicke Mathematik 1979, Wissenschaftsverlag des Bibliographischen Institus Mannheim, 43-62.

The condition number of the 21x21 Hilbert 30 matrix is approximately 10 , and is the Hilbert matrix of largest dimension exactly storable on that computer. To achieve this accuracy and, especially, to give only true results a precisely defined arithmetic is necessary. 0 with exactly representable operands. Therefore, we define a computer arithmetic in the first chapter. The theoretical background and the required algorithms for certain classes of problems are given in the succeeding chapters. The algorithms have been implemented on a minicomputer based on Z80 with a 64 k Byte memory.

Implementierung eines ALGOL-60 Systems mit Schrankenzahlen, Electron Datenverarb. 10, 189-194. Wolff von Gudenberg, J. Evaluation of the standard functions in generalized comput­ er arithmetic. Wolff von Gudenberg, J. (1980). Einbettung allgemeiner Rechnerarithmetik in Ulrich Kulisch 26 [29] [30] [31] PASCAL mittels eines Operatorkonzeptes und Implementierung der Standardfunktionen mit optimaler Genauigkeit. Dissertation, Universitat Karlsruhe. , et al. (1979). A proposed standard for floating-point arithmetic, SIGNUM Newsletter.

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