Condition the geometry of numerical algorithms Peter Bürgisser, Felipe Cucker

Format:

Book

Author/Creator:

Bürgisser, Peter, 1962- author.

Cucker, Felipe, 1958- author.

Series:

Grundlehren der mathematischen Wissenschaften 349

Language:

English

Subjects (All):

Numerical analysis.

Algorithms.

algorithms.

Medical Subjects:

Algorithms.

Physical Description:

1 online resource

Place of Publication:

Berlin Springer [2013]

Language Note:

English

System Details:

text file

PDF

Summary:

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

Contents:

Condition in Linear Algebra (). Normwise Condition of Linear Equation Solving Probabilistic Analysis Error Analysis of Triangular Linear Systems Probabilistic Analysis of Rectangular Matrices Condition Numbers and Iterative Algorithms Condition in Linear Optimization (). A Condition Number for Polyhedral Conic Systems The Ellipsoid Method Linear Programs and Their Solution Sets Interior-Point Methods The Linear Programming Feasibility Problem Condition and Linear Programming Optimization Average Analysis of the RCC Condition Number Probabilistic Analyses of the GCC Condition Number Condition in Polynomial Equation Solving (). A Geometric Framework for Condition Numbers Homotopy Continuation and Newton's Method Homogeneous Polynomial Systems Smale's 17th Problem: I Smale's 17th Problem: II Real Polynomial Systems Probabilistic Analysis of Conic Condition Numbers: I. The Complex Case Probabilistic Analysis of Conic Condition Numbers: II. The Real Case

Notes:

Includes bibliographical references and index

Print version record

Other Format:

Print version Bürgisser, Peter, 1962- Condition

ISBN:

9783642388965

3642388965

OCLC:

858626298

Access Restriction:

Restricted for use by site license