Numerical Software with Result Verification

Reliable computing techniques are essential if the validity of the output of a - merical algorithm is to be guaranteed to be correct. Our society relies more and more on computer systems. Usually, our systems appear to work successfully, but there are sometimes serious, and often minor, errors. Validated computing is one essential technology to achieve increased software reliability. Formal - gor in the de?nition of data types, the computer arithmetic, in algorithm design, and in program execution allows us to guarantee that the stated problem has (or does not have) a solution in an enclosing interval we compute. If the enclosure is narrow, we are certain that the result can be used. Otherwise, we have a clear warning that the uncertainty of input values might be large and the algorithm and the model have to be improved. The use of interval data types and al- rithms with controlled rounding and result veri?cation capture uncertainty in modeling and problem formulation, in model parameter estimation, in algorithm truncation, in operation round-o?, and in model interpretation. The techniques of validated computing have proven their merits in many scienti?c and engineering applications. They are based on solid and interesting theoretical studies in mathematics and computer science. Contributions from ?elds including real, complex and functional analysis, semigroups, probability, statistics,fuzzyintervalanalysis,fuzzylogic,automaticdi?erentiation,computer hardware, operating systems, compiler construction, programming languages, object-oriented modeling, parallel processing, and software engineering are all essential.

Inhalt

Languages.- OOP and Interval Arithmetic - Language Support and Libraries.- C-XSC 2.0 - A C++ Library for Extended Scientific Computing.- Software Systems and Tools.- Libraries, Tools, and Interactive Systems for Verified Computations Four Case Studies.- Multiple Precision Interval Packages: Comparing Different Approaches.- Interval Testing Strategies Applied to COSY's Interval and Taylor Model Arithmetic.- New Verification Techniques Based on Interval Arithmetic.- Nonlinear Parameter and State Estimation for Cooperative Systems in a Bounded-Error Context.- Guaranteed Numerical Computation as an Alternative to Computer Algebra for Testing Models for Identifiability.- Interval Algorithms in Modeling of Multibody Systems.- Reliable Distance and Intersection Computation Using Finite Precision Geometry.- On Singular Interval Systems.- Applications in Science and Engineering.- Result-Verifying Solution of Nonlinear Systems in the Analysis of Chemical Processes.- Verified Numerical Analysis of the Performance of Switching Systems in Telecommunication.- Result Verification for Computational Problems in Geodesy.- Global Optimization in the COCONUT Project.- An Application of Wavelet Theory to Early Breast Cancer.- Novel Approaches to Verification.- Using PVS to Validate the Inverse Trigonometric Functions of an Exact Arithmetic.- Novel Approaches to Numerical Software with Result Verification.- Static Analysis-Based Validation of Floating-Point Computations.