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Author : Owe Axelsson
Release : 2003
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Error Norm Estimation and Stopping Criteria in Preconditioned Conjugate Gradient Iterations by : Owe Axelsson
Download or read book Error Norm Estimation and Stopping Criteria in Preconditioned Conjugate Gradient Iterations written by Owe Axelsson. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Owe Axelsson
Release : 2000
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Error Norm Estimation and Stopping Criteria in Preconditioned Conjugate Gradient Iterations by : Owe Axelsson
Download or read book Error Norm Estimation and Stopping Criteria in Preconditioned Conjugate Gradient Iterations written by Owe Axelsson. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gérard Meurant
Release : 2024-01-30
Genre : Mathematics
Kind : eBook
Book Rating : 86X/5 ( reviews)
Book Synopsis Error Norm Estimation in the Conjugate Gradient Algorithm by : Gérard Meurant
Download or read book Error Norm Estimation in the Conjugate Gradient Algorithm written by Gérard Meurant . This book was released on 2024-01-30. Available in PDF, EPUB and Kindle. Book excerpt: The conjugate gradient (CG) algorithm is almost always the iterative method of choice for solving linear systems with symmetric positive definite matrices. This book describes and analyzes techniques based on Gauss quadrature rules to cheaply compute bounds on norms of the error. The techniques can be used to derive reliable stopping criteria. How to compute estimates of the smallest and largest eigenvalues during CG iterations is also shown. The algorithms are illustrated by many numerical experiments, and they can be easily incorporated into existing CG codes. The book is intended for those in academia and industry who use the conjugate gradient algorithm, including the many branches of science and engineering in which symmetric linear systems have to be solved.
Author : Raymond Chan
Release : 2007-02-22
Genre : Mathematics
Kind : eBook
Book Rating : 774/5 ( reviews)
Book Synopsis Milestones in Matrix Computation by : Raymond Chan
Download or read book Milestones in Matrix Computation written by Raymond Chan. This book was released on 2007-02-22. Available in PDF, EPUB and Kindle. Book excerpt: The text presents and discusses some of the most influential papers in Matrix Computation authored by Gene H. Golub, one of the founding fathers of the field. The collection of 21 papers is divided into five main areas: iterative methods for linear systems, solution of least squares problems, matrix factorizations and applications, orthogonal polynomials and quadrature, and eigenvalue problems. Commentaries for each area are provided by leading experts: Anne Greenbaum, Ake Bjorck, Nicholas Higham, Walter Gautschi, and G. W. (Pete) Stewart. Comments on each paper are also included by the original authors, providing the reader with historical information on how the paper came to be written and under what circumstances the collaboration was undertaken. Including a brief biography and facsimiles of the original papers, this text will be of great interest to students and researchers in numerical analysis and scientific computation.
Author : István Faragó
Release : 2013-12-10
Genre : Nature
Kind : eBook
Book Rating : 78X/5 ( reviews)
Book Synopsis Advanced Numerical Methods for Complex Environmental Models: Needs and Availability by : István Faragó
Download or read book Advanced Numerical Methods for Complex Environmental Models: Needs and Availability written by István Faragó. This book was released on 2013-12-10. Available in PDF, EPUB and Kindle. Book excerpt: High air pollution levels pose a significant threat to plants, animals and human beings. Efforts by researchers are directed towards keeping air pollution levels below well defined ‘critical‘ levels in order to maintain a sustainable atmosphere and environmental system. The application of advanced mathematical models is important for researchers to achieve this goal as efficiently as possible. Mathematical models can be used to predict answers to many important questions about the environment. This application comes with several complex theoretical and practical obstacles which need to be resolved. A successfully applicable mathematical model needs to enable researchers to • Mathematically describe all important physical and chemical processes. • Apply fast and sufficiently accurate numerical methods. • Ensure that the model runs efficiently on modern high speed computers. • Use high quality input data, both meteorological data and emission inventories, in the runs. • Verify the model results by comparing them with reliable measurements taken in different parts of the spatial domain of the model. • Carry out long series of sensitivity experiments to check the response of the model to changes of different key parameters. • Visualize and animate the output results in order to make them easily understandable even to non-specialists. This monograph thoroughly describes mathematical methods useful for various situations in environmental modeling - including finite difference methods, splitting methods, parallel computation, etc. - and provides a framework for resolving problems posed in relation to the points listed above. Chapters are written by well-known specialists making this book a handy reference for researchers, university teachers and students working and studying in the areas of air pollution, meteorology, applied mathematics and computer science.
