## Accuracy and Reliability in Scientific ComputingDeveloping accurate and reliable scientific software is notoriously difficult. This book investigates some of the difficulties related to scientific computing and provides insight into how to overcome them and obtain dependable results. The text deals thoroughly with the problems that affect software in general as well as the particular challenges of numerical computation: approximations occurring at all levels, continuous functions replaced by discretized versions, infinite processes replaced by finite ones, and real numbers replaced by finite precision numbers. Divided into three parts, it starts by illustrating some of the difficulties in producing robust and reliable scientific software. The second section describes diagnostic tools that can be used to assess the accuracy and reliability of existing scientific applications. In the last section, the authors describe a variety of techniques that can be employed to improve the accuracy and reliability of newly developed scientific applications. |

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### Contents

What Can Go Wrong in Scientific Computing? | 3 |

Assessment of Accuracy and Reliability | 13 |

Approximating Integrals Estimating Errors and Giving the Wrong Solution | 33 |

An Introduction to the Quality of Computed Solutions | 43 |

Qualitative Computing | 77 |

PRECISE and the Quality of Reliable Numerical Software | 95 |

Tools for the Verification of Approximate Solutions to Differential | 109 |

TECHNOLOGY FOR IMPROVING ACCURACY AND RELIABILITY | 123 |

The Use and Implementation of Interval Data Types | 173 |

Computerassisted Proofs and Selfvalidating Methods | 195 |

Hardwareassisted Algorithms | 241 |

Issues in Accurate and Reliable Use of Parallel Computing | 253 |

Softwarereliability Engineering of Numerical Systems | 265 |

301 | |

335 | |

in Java | 160 |

### Common terms and phrases

accuracy algorithm applications approximate solution arguments array backward error cache calculation CERFACS Check compiler complex components condition number correct cset data structures data types digits double precision dynamic eigenvalues equations error analysis estimate evaluation exact example execution fault fault-tolerant Figure finite floating-point arithmetic floating-point number floating-point operations Fortran 77 Fortran 95 function Gaussian elimination IEEE implementation integration interface interval analysis interval arithmetic interval data interval matrix INTLAB Java language LAPACK libraries linear algebra linear system loop Math mathematical MATLAB memory module multiplication numerical method Numerical Python numerical software NumPy optimization output package parallel computers parameter performance perturbation model pointer polynomial preprocessor problem processor produce Python real numbers result rounding routine runtime scientific computing self-validating methods software reliability solving specification standard techniques Theorem validation variables vector verification zero