This collection of papers on scientific computing with validation covers the design of floating point units, algorithms for floating point operations, and elementary function evaluations with maximum accuracy. Scientific computing methods are discussed for areas of applied mathematics such as numerical linear algebra, nonlinear equations, global optimization, ordinary and partial differential equations and dynamical systems. Some computer science aspects like complexity are also considered, as are examples where validation methods have successfully been used in applications from the engineering sciences.
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ISBN-13
978-3-05-501737-7 (9783055017377)
Schweitzer Klassifikation
Partial table of contents:; HARDWARE AND FLOATING POINT OPERATIONS; Hardware Reciprocal Table Compression/Decompression Techniques (D. Sarma & D. Matula); Hardware Support for Interval Arithmetic (J. von Gudenberg); FUNCTION EVALUATION; Shared Computations for Efficient Interval Function Evaluation ( E. Hyvvnen & S. De Pascale); Computing Narrow Inclusions for Cauchy Principal Value Integrals (W. Krdmer & S. Wedner); SOFTWARE; Processing Software Metrics in an Integrated Development Environment for Pascal-XSC (H. Berlejung); LINEAR ALGEBRA; Success in Epsilon-Inflation (G. Mayer); NONLINEAR EQUATIONS; Effective Improvements of the Interval-Newton-Method (G. Alefeld, et al.); On the Application of an Interval Algorithm for Set Inversion (M. Candev); A Parallel Algorithm for Enclosing All Zeros of a Nonlinear System of Equations (A. Wiethoff); OPTIMIZATION; A Parallel Method for Verified Global Optimization (S. Berner); DIFFERENTIAL EQUATIONS; Validating an A Priori Enclosure Using High-Order Taylor Series (G. Corliss & R. Rihm); Inheritable Properties and Computer Assisted Proofs in Dynamics (M. Mrozek); COMPLEXITY AND THEORY OF INTERVAL PROBLEMS; On the Foundations of Interval Arithmetic (S. Markov); APPLICATIONS IN ENGINEERING; Application of Automatic Differentiation Techniques to Circuit Simulation (H.-J. Dobner & W. Klein).
