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By Ulrich W. Kulisch, Willard L. Miranker

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Rump, S. , Kaucher, E. (1980). Small bounds for the solution of systems of linear equations, Computing Suppl. 2, 157-164. Rump, S. M. (1980). Kleine Fehlerschranken bei Matrixproblemen, Dissertation, Universitat Karlsruhe. Rump, S. M. (1980). 5, S. 243-244. -W. (1968). 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.

The minicomputer has been developed at the Institute for Applied Mathematics at the University of Karlsruhe and the Fachbereich Informatik of the University at Kaiserslautern (Professors Kulisch and Wippermann). Further, the algorithms are implemented on a UNIVAC 1108 and IBM 370/168. However, we cannot mention every detail of the implementation in the succeeding description of the algorithms. We give explicit algorithms for solving systems of linear equations and systems of nonlinear equations and the verification of the nonsingularity of a 54 Siegfried M.

4142200 45 Computer Demonstration Packages • 8 » C Give the range w h e n the polynomial shall be displayed. 4142200 * E Enter an approximation for a zero. 41421356237E+00* there is one and only one zero of the polynomial in use. 41421568627E+00, there is one and only one zero of the polynomial in use. 41421568&28E+00] ♦ Q Evaluating the polynomial using Horner's scheme in floating-point arithmetic gives a discontinuous graph of the function. Using the new algorithm even shows two zeros of the polynomial.

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