Condition / Grundlehren der mathematischen Wissenschaften Bd.349 (PDF)

Peter Bürgisser is an internationally recognized expert in complexity theory. He is associate editor of the journal Computational Complexity and he was invited speaker at the 2010 International Congress Mathematicians. Felipe Cucker is well known for his work on complexity over the real numbers, jointly with L. Blum, S. Smale and M. Shub. He also worked in learning theory and made seminal contributions to condition numbers in optimization and their probabilistic analyses. F.C. is former chair of the Society for the Foundations of Computational Mathematics and the current managing editor of the society's journal.

“The book under review is divided intothree parts, ‘which approximately correspond to themes of conditioning inlinear algebra, linear programming, and polynomial equation solving’. … Givenits detailed covering of a wide range of topics and its geometric approach, Ithink this book may well become a must-have for all who are seriouslyinterested in numerical algorithms.” (S. C. Coutinho, The Mathematical Gazette,Vol. 99 (546), November, 2015)

“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. … The book is self contained and easy to read … . The book ends with the statement of eighteen open problems that shows that Mr. Condition has a bright future ahead of him.” (Jean-Claude Yakoubsohn, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 117, 2015)

“The authors intend with this book to fill the gap by addressing the probabilistic analysis of the algorithms related to condition numbers. … Under the vigilant eyes of so many famous scientists, it is sure that this book is a milestone in this area of research. … The monograph under review is without any doubt a very carefully prepared one, and researchers interested in numerical analysis (and related topics) should become familiar with this book.” (Elena Pelican, Mathematical Reviews, August, 2014)

“This book studies a type of numerical imprecision that arises universally. … Bürgisser (Technical Univ. of Berlin, Germany) and Cucker (City Univ. of Hong Kong) provide the first book-length treatment of the concept. … Summing Up: Recommended. Upper-division undergraduates through researchers/faculty.” (D. V. Feldman, Choice, Vol. 51 (11), July, 2014)

“The authors of this book discuss the ways that such errors are produced in a computer, and consider the use of condition numbers to understand the performance of