Condition - The Geometry of Numerical Algorithms
Condition - The Geometry of Numerical Algorithms
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DOI：
10.1007/978-3-642-38896-5
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发表时间：
2013-08
期刊：
影响因子：
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通讯作者：
Peter Bürgisser;F. Cucker
中科院分区：
文献类型：
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作者：
Peter Bürgisser;F. Cucker
这本书收集了跨越不同数学学科演变成无缝叙事的线索。它涉及的条件作为一个主要方面的理解性能---关于稳定性和复杂性---数值算法。虽然条件的作用是在过去半个世纪形成的，但迄今为止还没有一本专著以统一和系统的方式处理这个问题。这本书特别强调通过分析相应的条件数值算法的概率分析。博览会的水平增加沿着书，开始在线性代数的背景下，在本科水平，并达到在其第三部分的最新发展和部分解决斯梅尔的第17个问题，可以解释在研究生课程。它的中间部分包含一个基于条件的线性规划课程，填补了基于单纯形法和凸规划的主题之间的空白。
This book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspect in the understanding of the performance---regarding both stability and complexity---of numerical algorithms. While the role of condition was shaped in the last half-century, so far there has not been a monograph treating this subject in a uniform and systematic way. The book puts special emphasis on the probabilistic analysis of numerical algorithms via the analysis of the corresponding condition. The exposition's level increases along the book, starting in the context of linear algebra at an undergraduate level and reaching in its third part the recent developments and partial solutions for Smale's 17th problem which can be explained within a graduate course. Its middle part contains a condition-based course on linear programming that fills a gap between the current elementary expositions of the subject based on the simplex method and those focusing on convex programming.