This volume contains mainly a collection of the invited lectures which were given during a conference on "Fundamentals of Numerical Computation", held in June, 5 - 8, 1979, on the occasion of the centennial of the Technical University of Berlin. About hundred scientists from several countries attended this conference. A preceding meeting on "Fundamentals of Computer-Arithmetic" was held in August, 1975, at the "Mathematisches Forschungsinstitut Oberwolfach". The lectures of this conference have been published as Supplementum 1 of Computing (Editors R. Albrecht, U. Kulisch). After a period of four years of active research the purpose of the Berlin-Conference was to give a broad survey of the present status of the closely connected topics Interval Analysis, Mathematical Foundation of Computer Arithmetic, Rounding Error Analysis and Stability of Numerical Algorithms and to give prospects of future activities in these fields. Besides the invited lectures 35 short com- munications, each of 20 minutes length, were given. We gratefully acknowledge the support of the President of the Technical University and of his Aussenreferat as well as of the Department of Mathematics. Besides these institutions financial support was given by AEG-Telefunken, Berlin, Allianz Lebensversicherungs A.G., Stuttgart, CDC, Hamburg/Berlin, DAT A 100, Munchen, Gesellschaft von Freunden der TU Berlin e.V., Berlin and Siemens AG., Berlin. Finally we express our thanks to Mrs. G. Froehlich and Mrs. B. Trajanovic, who managed the paper work before, during and after the conference. Front Matter....Pages i-vii On Methods for the Construction of the Boundaries of Sets of Solutions for Differential Equations or Finite-Dimensional Approximations with Input Sets....Pages 1-16 Roundings and Approximations in Ordered Sets....Pages 17-31 Interval Analysis in the Extended Interval Space IR ....Pages 33-49 Arithmetic Operations in Interval Spaces....Pages 51-67 Some Applications of Extended Interval Arithmetic to Interval Iterations....Pages 69-84 Foundations of Finite Precision Rational Arithmetic....Pages 85-111 Interval Methods for Nonlinear Systems....Pages 113-120 Algorithms for Multiplication with Given Precision....Pages 121-129 Unrestricted Algorithms for Generating Elementary Functions....Pages 131-140 Applications of Software for Automatic Differentiation in Numerical Computation....Pages 141-156 Small Bounds for the Solution of Systems of Linear Equations....Pages 157-164 Shorthand Notation for Rounding Errors....Pages 165-168 Rounding Error Analysis of Elementary Numerical Algorithms....Pages 169-195 Iterative Methods in the Spaces of Rounded Computations....Pages 197-209 Portable Software for Interval Arithmetic....Pages 211-229
