Condition : the geometry of numerical algorithms / Peter Bürgisser, Felipe Cucker

In the book, a unified view on the condition of problems is given. The book consists of three parts: condition in linear algebra, condition in linear optimization, and condition in polynomial equation solving. Part I starts with a short course on the condition of linear equation solving and probability theory. Then, for example, an error analysis of triangular linear systems and a probabilistic analysis of systems with a rectangular matrix are given. The role of condition numbers in iterative algorithms is discussed. Methods for solving optimization problems (ellipsoid method, interior-point methods) are explained and analysed in Part II. In the third part, a geometric framework for condition numbers is given. Newton’s method, Smale’s 17th problem, and real polynomial systems are investigated. (Zentralblatt)