## C++ Toolbox for Verified Computing I: Basic Numerical Problems Theory, Algorithms, and ProgramsOur aim in writing this book was to provide an extensive set of C++ programs for solving basic numerical problems with verification of the results. This C++ Toolbox for Verified Computing I is the C++ edition of the Numerical Toolbox for Verified Computing l. The programs of the original edition were written in PASCAL-XSC, a PASCAL eXtension for Scientific Computation. Since we published the first edition we have received many requests from readers and users of our tools for a version in C++. We take the view that C++ is growing in importance in the field of numeri cal computing. C++ includes C, but as a typed language and due to its modern concepts, it is superior to C. To obtain the degree of efficiency that PASCAL-XSC provides, we used the C-XSC library. C-XSC is a C++ class library for eXtended Scientific Computing. C++ and the C-XSC library are an adequate alternative to special XSC-Ianguages such as PASCAL-XSC or ACRITH-XSC. A shareware version of the C-XSC library and the sources of the toolbox programs are freely available via anonymous ftp or can be ordered against reimbursement of expenses. The programs of this book do not require a great deal of insight into the features of C++. Particularly, object oriented programming techniques are not required. |

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### Contents

Introduction | 1 |

The Features of CXSC | 17 |

Mathematical Preliminaries | 30 |

Copyright | |

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### Common terms and phrases

Accu accuracy Algorithm approximation automatic differentiation basic index set bisection C-XSC complex interval components compute enclosures const int const real& cout defined Deriv Type DerivOrder DerivType& differentiation arithmetic division by zero dot product elementary functions elements EmptyList enclosed endl epsilon inflation error code error message extended interval extended interval Newton FreeList friend DerivType friend HessType function f function value Global functions global minimizer global minimum value global optimization gradient GradType GradType& GTvector header file Hessian Hessian matrix HessOrder HessType& IAccu implementation InfoVector input int& integer interval arithmetic interval Newton step interval vector interval& inverse Jacobian kmax linear programming linear system matrix MaxCount maximum number method midpoint module Newton's method nmax nonlinear number of iterations operands operator operator+ Pair Parameters problem propagate domain error Resize return res Staggered& starting interval static unique variable verified