Skip to content
Register Sign in Wishlist
Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs

Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs

$39.00 (P)

  • Date Published: October 2016
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9781611973839

$ 39.00 (P)
Paperback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Unavailable Add to wishlist

Looking for an examination copy?

This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact collegesales@cambridge.org providing details of the course you are teaching.

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • The route from an applied problem to its numerical solution involves modeling, analysis, discretization, and the solution of the discretized problem. This book concerns the interplay of these stages and the challenges that arise. The authors link analysis of PDEs, functional analysis, and calculus of variations with iterative matrix computation using Krylov subspace methods. While preconditioning of the conjugate gradient method is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system, the authors develop connections between preconditioning and PDEs. Additionally, links between the infinite-dimensional formulation of the conjugate gradient method, its discretization and preconditioning are explored. The book is intended for mathematicians, engineers, physicists, chemists, and any other researchers interested in the issues discussed. Aiming to improve understanding between researchers working on different solution stages, the book challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.

    • A novel approach, connecting preconditioning with PDE analysis and the infinite-dimensional formulation of the conjugate gradient method
    • Challenges commonly held views, addresses widespread misunderstandings
    • Formulates thought-provoking open questions for further research
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: October 2016
    • format: Paperback
    • isbn: 9781611973839
    • length: 114 pages
    • dimensions: 155 x 175 x 7 mm
    • weight: 0.22kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Preface
    1. Introduction
    2. Linear elliptic partial differential equations
    3. Elements of functional analysis
    4. Riesz map and operator preconditioning
    5. Conjugate gradient method in Hilbert spaces
    6. Finite dimensional Hilbert spaces and the matrix formulation of the conjugate gradient method
    7. Comments on the Galerkin discretization
    8. Preconditioning of the algebraic system as transformation of the discretization basis
    9. Fundamental theorem on discretization
    10. Local and global information in discretization and in computation
    11. Limits of the condition number-based descriptions
    12. Inexact computations, a posteriori error analysis, and stopping criteria
    13. Summary and outlook
    Bibliography
    Index.

  • Authors

    Josef Málek, Charles University, Prague
    Josef Málek is a Professor at the Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic. He is a director of the Nečas Center for Mathematical Modeling and head of the Department of Mathematical Modeling, comprising researchers with diverse backgrounds focused upon the graduate study program 'Mathematical modeling in science and technology'. His research primarily concerns mathematical analysis of nonlinear PDEs stemming from non-Newtonian fluid mechanics, and he has contributed to the constitutive theory in the fluid and solid mechanics and in the theory of mixtures. His research approach emphasizes the need for interactions between modeling, analysis, scientific computing, and experiments.

    Zdeněk Strakoš, Charles University, Prague
    Zdenek Strakos is a Professor at the Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic. He has been an active member of several professional committees and journal editorial boards. He served on the ERC Advanced Grants Evaluation Panel for Computer Science and Informatics and was named its Chair in 2014. He was awarded the SIAM Activity Group on Linear Algebra Prize (1994), the Annual Prize of the Academy of Sciences of the Czech Republic (2007), and the Bernard Bolzano Medal of the Academy of Sciences of the Czech Republic for Merits in Mathematical Sciences (2013). In 2014 he was selected as a SIAM Fellow for advances in numerical linear algebra, especially iterative methods. He is interested in looking for interconnections between problems and disciplines, and in viewing particular questions in a wide context.

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon
×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×