C++ toolbox for verified computing 1
This C++ Toolbox for Verified Computing presents an extensive set of sophisticated tools for solving basic numerical problems with verification of the results. It is the C++ edition of the Numerical Toolbox for VerifiedComputingwhich was based on the computer language PASCAL-XSC. The sources of the programs in this book are freely available via anonymous ftp. This book offers a general discussion on arithmetic and computational reliability, analytical mathematics and verification techniques, algorithms, and (most importantly) actual C++ implementations. In each chapter, examples, exercises, and numerical results demonstrate the application of the routines presented.
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The Features of CXSC
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Accu Algorithm approximation automatic differentiation basic index set bisection C-XSC char complex interval components compute enclosures const int const realft constructors cout defined DerivOrder DerivType DerivType operator DerivType res DerivTypeft differentiation arithmetic division by zero dot product elementary functions elements EmptyList endl epsilon inflation error code error message extended interval extended interval Newton FreeList friend DerivType friend friend friend function value Global functions global minimizer global minimum value global optimization gradient GradOrder GradTypeft GTvector Halley's method header file Hessian Hessian matrix HessOrder HessType HessType HessType HessTypeft imatrixft implementation input integer interval arithmetic interval Newton step interval vector intervalft intft inverse ivectorft Jacobian kmax linear programming linear system MaxCount maximum number method midpoint Newton's method nmax NoError number of iterations operands operator+ optimal basic index PairlPtr Parameters propagate domain error res.ddf res.f res(u.nmax Resize return res starting interval u.nmax variable verification step zero