Issue No. 07 - July (1977 vol. 26)
U. Kulisch , Institute of Applied Mathematics, University of Karlsruhe
During recent years a number of papers concerning a mathematical foundation of computer arithmetic have been written. Some of these papers are still unpublished. The papers consider the spaces which occur in numerical computations on computers depending on a properly defined computer arithmetic. The following treatment gives a summary of the main ideas of these papers. Many of the proofs had to be sketched or completely omitted. In such cases the full information can be found in the references.
Axiomatic definition of computer arithmetic, floating-point arithmetic, interval arithmetic, numerical analysis, rounding analysis, theory and implementation of computer arithmetic.
U. Kulisch, "Mathematical Foundation of Computer Arithmetic", IEEE Transactions on Computers, vol. 26, no. , pp. 610-621, July 1977, doi:10.1109/TC.1977.1674893