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By Ulrich W. Kulisch, Willard L. Miranker

ISBN-10: 0124286607

ISBN-13: 9780124286603

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REALIZATION AND APPLICATIONS A complete implementation of the arithmetic operations by semimorphism in all spaces of Figure 1 was first executed at the author's institute between 1977 and 1979. This imple­ mentation uses a Z80 microprocessor. Other implementations on more powerful processors have been finished in the meantime as well. language. PASCAL is used as the basic programming In order to avoid the disadvantages of the vertical definition of the arithmetic operations the programming language PASCAL was extended by a general operator concept.

The algorithms have been implemented on a minicomputer based on Z80 with a 64 k Byte memory. There, a decimal arithmetic with 12 digits in the mantissa and a PASCAL-SC compiler is implemented. 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.

77350269192E-013 38 Siegfried M. Rump Rounding error and cancellation A graph of the following polynomial will be displayed: 2 0 2 0 X * * 4 - 5 7 4 1 X * * 3 - J C * * 2 + 1 1 4 8 2 J C - 8 118. The polynomial will be evaluated using Horner's scheme in floating-point arithmetic. Give the degree of the polynomial to be displayed and then the coefficients starting with the leading coefficient. * 4 * 2030 -5741 -1 11482 -8118 Give the range where the polynomial shall be displayed. 4200 Computer Demonstration Packages 39 Give a new rangei give P for a new polynomial or Q for quit.

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

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