A Note on the Convergence of Alternating Direction Methods (Classic Reprint)
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
£ 13.12
Quantity: Over 20 available
Add to basketItem description from seller
Print on Demand. This book delves into alternating direction methods, a crucial numerical approach to solving elliptic difference equations. These equations arise commonly in many fields. The author provides a comprehensive analysis of the convergence rates for two fundamental alternating direction methods: the Douglas-Rachford method and the Peaceman-Rachford method. Notably, these methods are applicable to a broad range of elliptic equations with variable coefficients defined in arbitrary regions. The author goes beyond existing proofs to develop novel estimates, demonstrating that the error in the solution is reduced significantly with each iteration, providing valuable insights into the effectiveness of these methods. The book's findings advance our understanding of alternating direction methods, solidifying their importance as powerful tools for solving elliptic equations. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.…
Seller Inventory # 9780243082995_0
- Title
- A Note on the Convergence of Alternating Direction Methods (Classic Reprint)
- Author
- Milton Lees
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 0243082991
- ISBN 13
- 9780243082995
- Seller catalogs
- Calculus
Convergence of the Single parameter alternating direction methods of Douglas, Peaceman, and Rachford [3] has been proved for a wide class of elliptic difference equations; see, for example, Birkhoff and varga The proof consists in showing that a certain matrix, similar to the defining matrix, has spectral radius less than one. Since the defining matrices for these methods are symmetric only when they are induced by a proper discretization of Iaplace's equation in a rectangular region, an estimate for their spectral radii does not imply a corresponding norm estimate for their rate of convergence.
The purpose of this note is to present another proof of the convergence of the two basic alternating direction methods which, at the same time, provides a norm estimate for their rate of convergence. First, for simplicity, we shall consider Laplaceis equation in an arbitrary, bounded lattice region.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
"Synopsis" may belong to another edition of this title.
Forgotten Books
London, United Kingdom
AbeBooks seller since June 2, 2021
Shipping rates from United Kingdom to U.S.A.
| Item | 5 to 10 business days | 5 to 10 business days |
|---|---|---|
| First item | £ 0.00 | £ 0.00 |
Payment methods
Store description
Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
Specialty
TradeSeller's business information
FB &c Ltd
Dalton House, 60 Windsor Avenue
London, United Kingdom SW19 2RR
Terms of sale
Forgotten Books publishes hundreds of thousands of rare and classic books.
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
This text has been digitally restored from a historical edition. Some errors may persist, however we consider it worth publishing due to the work's historical value.
The digital edition of all books may be viewed before purchase if you request a sample.
Right of withdrawal
If you are a consumer you can withdraw from the contract in accordance with the following. Consumer means any natural person who is acting for purposes which are outside his trade, business, craft or profession.
Information regarding the right of withdrawal
Statutory right to withdraw
You have the right to withdraw from this contract within 14 days without giving any reason.
The withdrawal period will expire after 14 days from the day on which you acquire, or a third party other than the carrier and indicated by you acquires, physical possession of the last good or the last lot or piece.
To exercise the right of withdrawal, electronically fill in and submit a clear statement on our website, under "My Purchases" in "My Account". We will communicate to you an acknowledgement of receipt of such a withdrawal on a durable medium (e.g. by e-mail) without delay.
To meet the withdrawal deadline, it is sufficient for you to send your communication concerning your exercise of the right of withdrawal before the withdrawal period has expired.
Effects of withdrawal
If you withdraw from this contract, we will reimburse to you all payments received from you, including the costs of delivery (except for the supplementary costs arising if you chose a type of delivery other than the least expensive type of standard delivery offered by us).
We may make a deduction from the reimbursement for loss in value of any goods supplied, if the loss is the result of unnecessary handling by you.
We will make the reimbursement without undue delay, and not later than 14 days after the day on which we are informed about your decision to withdraw from this contract.
We will make the reimbursement using the same means of payment as you used for the initial transaction, unless you have expressly agreed otherwise; in any event, you will not incur any fees as a result of such reimbursement.
We may withhold reimbursement until we have received the goods back, or you have supplied evidence of having sent back the goods, whichever is the earliest.
You shall send back the goods or hand them over to Forgotten Books, London, United Kingdom, without undue delay and in any event not later than 14 days from the day on which you communicate your withdrawal from this contract to us. The deadline is met if you send back the goods before the period of 14 days has expired. You will have to bear the direct cost of returning the goods. You are only liable for any diminished value of the goods resulting from the handling other than what is necessary to establish the nature, characteristics and functioning of the goods.
Exceptions to the right of withdrawal
The right of withdrawal does not apply to:
- The delivery of newspapers, journals or magazines with the exception of subscription contracts; and
- The supply of digital content which is not supplied on a tangible medium (e.g. on a CD or DVD) if you accepted when you placed your order that we could start to deliver it, and that you could not withdraw once delivery had started.
Shipping terms
We are committed to minimizing our environmental impact and reducing shipping costs by manufacturing and shipping our products as close to our customers as possible. For orders within the United States, your items are shipped from the USA. UK orders are fulfilled from the UK, while European orders are shipped from a location within Europe. Canadian orders may be shipped from either Canada or the USA, depending on the size of the order.
For our customers in other regions around the world, we ensure that your orders are shipped from the closest available location to reduce delivery times and carbon footprint. Our goal is to deliver your products efficiently, no matter where you are located.
Please be aware that depending on the size of your order and local legislation in your country, there may be additional taxes, customs duties, and fees imposed by the destination country. These charges are not included in the item price or shipping cost. They are the responsibility of the customer and must be paid upon delivery.
We recommend checking with your local customs office for more information on potential charges before placing your order. Forgotten Books is not responsible for any customs duties, taxes, or fees incurred.