The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations

Description

"No present book comes near this one in the range and depth of treatment of these two extremely important methodsthe Lanczos algorithm and the method of conjugate gradients." Chris Paige, School of Computer Science, McGill University. The Lanczos and conjugate gradient (CG) algorithms are fascinating numerical algorithms. This book presents the most comprehensive discussion to date of the use of these methods for computing eigenvalues and solving linear systems in both exact and floating point arithmetic. The author synthesizes the research done over the past 30 years, describing and explaining the "average" behavior of these methods and providing new insight into their properties in finite precision. Many examples are given that show significant results obtained by researchers in the field. The author emphasizes how both algorithms can be used efficiently in finite precision arithmetic, regardless of the growth of rounding errors that occurs. He details the mathematical properties of both algorithms and demonstrates how the CG algorithm is derived from the Lanczos algorithm. Loss of orthogonality involved with using the Lanczos algorithm, ways to improve the maximum attainable accuracy of CG computations, and what modifications need to be made when the CG method is used with a preconditioner are addressed. This book is intended for applied mathematicians, computational scientists, engineers, and physicists who have an interest in linear algebra, numerical analysis, and partial differential equations. It will be of interest to engineers and scientists using the Lanczos algorithm to compute eigenvalues and the CG algorithm to solve linear systems, and to researchers in Krylov subspace methods for symmetric matrices, especially those concerned with floating point error analysis. Moreover, it can be used in advanced courses on iterative methods or as a comprehensive presentation of a well-known numerical method in finite precision arithmetic. Contents Preface; Chapter 1: The Lanczos algorithm in exact arithmetic; Chapter 2: The CG algorithm in exact arithmetic; Chapter 3: A historical perspective on the Lanczos algorithm in finite precision; Chapter 4: The Lanczos algorithm in finite precision; Chapter 5: The CG algorithm in finite precision; Chapter 6: The maximum attainable accuracy; Chapter 7: Estimates of norms of the error in finite precision; Chapter 8: The preconditioned CG algorithm; Chapter 9: Miscellaneous; Appendix; Bibliography; Index.

Disclaimer:
Contents of this page are indexed from the Internet. All actions are under your responsability. Email us to report illegal contents or external links and we'll remove them immediately.

Please check the description for download links if any or do a search to find alternative books.

Can't Download?
Please search mirrors if you can't find download links for "The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations" in "Description" and someone else may update the links. Check the comments when back to find any updates.

Search Mirrors
Maybe some mirror pages will be helpful, search this book at top of this page or click here to find more info.

1. Ebooks list page : 2013
2. [share_ebook] The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations
3. Lanczos Algorithms for Large Symmetric Eigenvalue Computations Volume 1: Theory (Classics in Applied Mathematics)
4. Conjugate Gradient Algorithms in Nonconvex Optimization
5. Conjugate Gradient Algorithms in Nonconvex Optimization {Repost }
6. Lectures on Finite Precision Computations (Software, Environments, and Tools)
7. Parameter Sensitivity in Nonlinear Mechanics: Theory and Finite Element Computations
8. Fundamental Finite Element Analysis and Applications: with Mathematica and Matlab Computations
9. Algorithms and Computations
10. Theory of Periodic Conjugate Heat Transfer
11. Parallel Algorithms for Matrix Computations
12. Precision Woods and Long Iron Shots (Precision Golf Series)
13. Matrix Algebra: Theory, Computations, and Applications in Statistics
14. Matrix Algebra: Theory, Computations, and Applications in Statistics
15. Precision Crystallization: Theory and Practice of Controlling Crystal Size
16. Topics in Validated Computations: Proceedings of Imacs-Gamm International Workshop on Validated Computations