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The Unavoidable Condition… A Report on the Book

机译：不可避免的情况…书上的报告

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I remember my first numerical experiments using computers and the shout of joy after lots of attempts: "it works". But disappointment came soon enough due to the inconsistency and lack of understanding of the numerical results. The first reaction was to believe that the computer code contains errors. But with time, coding errors disappear while numerical instabilities remain. Only theoretical conditions allow us to understand the mechanism of numerical errors. It was the book of Gastinel [5] that introduced me to the notion of condition. The terminology of condition number or conditioning is also used without distinction. Then, I understood that the computer was not the only one responsible for errors but the problem itself could contain the seeds of numerical disasters. The number of papers with condition number in the title is very huge and, it is very surprising that this book published in 2013 is the first book devoted entirely on this subject. It must be said that this book is a full success since it realizes a synthesis of ideas and works on the mathematical foundations on conditioning. First of all, I will say that I enjoyed the general spirit of the book explaining the points of view from which are discussed various aspects of condition. By the way, I will explain how Smale's 17th problem has stimulated research in this area and strengthened connections between algebraic geometry, integral geometry, probability and numerical analysis.
机译：我记得我第一次使用计算机进行的数值实验，经过多次尝试后欢呼雀跃：“有效”。但是由于不一致和对数值结果缺乏理解，失望很快就来了。第一个反应是认为计算机代码包含错误。但是随着时间的流逝，编码错误消失了，而数值不稳定仍然存在。只有理论条件才能让我们理解数值误差的机理。正是加斯泰尼尔（Gastinel）[5]这本书向我介绍了条件的概念。条件编号或条件的术语也可以不加区别地使用。然后，我知道计算机不是唯一负责错误的计算机，但问题本身可能包含数字灾难的种子。标题中带有条件编号的论文数量非常之多，令人惊讶的是，2013年出版的这本书是第一本专门针对该主题的书籍。必须说这本书是完全成功的，因为它实现了思想的综合并在条件的数学基础上进行了研究。首先，我要说的是，我很喜欢这本书的总体精神，它解释了观点，并从中讨论了状况的各个方面。顺便说一下，我将解释Smale的第17个问题如何激发了这一领域的研究，并加强了代数几何，积分几何，概率和数值分析之间的联系。

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