作者: | |
ISBN: | 9789811286469 |
出版社: | |
出版日期: | 2024/05/24 |
內文簡介
The Numerical Jordan Form is the first book dedicated to exploring the algorithmic and computational methods for determining the Jordan form of a matrix, as well as addressing the numerical difficulties in finding it. Unlike the 'pure' Jordan form, the numerical Jordan form preserves its structure under small perturbations of the matrix elements so that its determination presents a well-posed computational problem. If this structure is well conditioned, it can be determined reliably in the presence of uncertainties and rounding errors.
This book addresses the form's application in solving some important problems such as the estimation of eigenvalue sensitivity and computing the matrix exponential. Special attention is paid to the Jordan–Schur form of a matrix which, the author suggests, is not exploited sufficiently in the area of matrix computations. Since the mathematical objects under consideration can be sensitive to changes in the elements of the given matrix, the book also investigates the perturbation analysis of eigenvalues and invariant subspaces. This study is supplemented by a collection over 100 M-files suitable for MATLAB in order to implement the state-of-the art algorithms presented in the book for reducing a square matrix into the numerical Jordan form.
Researchers in the fields of numerical analysis and matrix computations and any scientists who utilise matrices in their work will find this book a useful resource, and it is also a suitable reference book for graduate and advance undergraduate courses in this subject area.
Contents:
- Preface
- List of Algorithms
- Notation
- Numerical Matrix Computations
- The Eigenvalue Problem
- The Eigenvalue Sensitivity Problem
- Numerical Solution of the Eigenvalue Problem
- Geometry of Jordan Forms
- Reduction into Jordan–Schur Form
- Reduction into Weyr and Jordan Forms
- Case Study 1: Eigenvalue Sensitivity Analysis
- Case Study 2: Computing the Matrix Exponential
- Appendix: Review of Linear Algebra and Matrix Analysis
- Bibliography
- Index
Readership: This book is suitable for practitioners and researchers in the fields of numerical analysis, matrix computations and applied mathematics, as well as scientists more broadly who use matrices in their work. It would also be suitable as a textbook or reference book for graduate and advanced undergraduate student courses related to numerical analysis, computation or numerical linear algebra, and matrix computations.
Key Features:- The first book entirely devoted to the numerical computation of Jordan and Weyr canonical forms
- Considers for the first time in detail the Jordan–Schur form of a matrix and its application to the solution of several matrix problems
- Contains 100 numerical algorithms implemented as M-files for MATLAB as supplementary material
- Contains many numerical examples and figures illustrating the algorithms implementation and their behavior
- May be used as a reference on Numerical Matrix Computations or for a MSc course on Advanced Matrix Computations
Kobo 電子書 購買注意事項如下:
(一)如果您是第一次購買Kobo電子書的顧客,請依以下兩種購買方式擇一進行綁定:
1.PChome 24h 網頁版(https://24h.pchome.com.tw/):結帳後至顧客中心,確認訂單狀態,若為確認中,請稍候五分鐘,待訂單狀態變為訂單成立後,點選明細,在訂單資訊中點選〔內容〕,在彈跳視窗後點選〔去兌換〕,即可前往Kobo官網執行綁定及登入流程。
我的訂單/顧客中心 >訂單查詢> 訂單編號> 點選明細 > 訂單資訊 點選〔內容〕>彈跳視窗 點選〔去兌換〕即可前往Kobo官網執行綁定及登入流程。
2.PChome APP版:結帳後至顧客中心,確認訂單狀態,若為確認中,請稍候五分鐘,待訂單狀態變為訂單成立後,點選明細,在訂單資訊中點選[序號/軟體下載],並在彈跳視窗出現後點選〔下載連結〕,即可前往Kobo官網執行綁定及登入流程。
顧客中心> 訂單查詢> 訂單編號> 點選明細 > 訂單資訊 點選 [序號/軟體下載] >彈跳視窗 點選〔下載連結〕即可前往Kobo官網執行綁定及登入流程。
*進入Kobo官網後的綁定流程請參考如下:
(使用Kobo主帳號 登入/註冊)
1. 當您在PChome 24h 網頁版(https://24h.pchome.com.tw/)/PChome APP版,購買確認後,並依步驟跳轉到Kobo官網時,下滑點選〔更多登錄選項〕,由〔PChome〕後點選進入,同意後登入,並可以註冊Kobo主帳號進行綁定,完成後,所購買的書籍即會出現在Kobo APP/Kobo 閱讀器/Kobo官網內的我的書籍。(使用快速登入:FACEBOOK、GOOGLE、APPLE帳號登入)
2. 當您在PChome 24h 網頁版(https://24h.pchome.com.tw/)/PChome APP版,購買確認後,並依指示跳轉到Kobo官網時,點選〔FACEBOOK、GOOGLE、APPLE帳號登入〕擇一登入,同意後登入,並可以註冊Kobo主帳號進行綁定,完成後,所購買的書籍即會出現在Kobo APP/Kobo 閱讀器/Kobo官網內的我的書籍。(二)如果您是已經完成PChome與Kobo帳號綁定程序,非第一次購買Kobo電子書的顧客
1.PChome 24h 網頁版(https://24h.pchome.com.tw/):結帳後至顧客中心,確認訂單狀態,若為確認中,請稍候五分鐘,待訂單狀態變為訂單成立後,點選明細,在訂單資訊中點選〔內容〕,在彈跳視窗後點選〔去兌換〕,所購買的書籍即會出現在Kobo APP/Kobo 閱讀器/Kobo官網內的我的書籍。
2.PChome APP版:結帳後至顧客中心,確認訂單狀態,若為確認中,請稍候五分鐘,待訂單狀態變為訂單成立後,點選明細,在訂單資訊中點選[序號/軟體下載],並在彈跳視窗出現後點選〔下載連結〕,所購買的書籍即會出現在Kobo APP/Kobo 閱讀器/Kobo官網內的我的書籍。
- 退換貨:依樂天Kobo官方規範為準
- 僅能由 閱讀器以外 的裝置做會員帳號綁定
- 請注意,帳號綁定後:
* Kobo會更新您的帳戶詳細資料
* 您將能在Kobo APP/Kobo 閱讀器/Kobo官網中查看所有書籍
* 帳號綁定後,您可以使用任一帳戶登入 Kobo
* 完成第一次串接時,請登出所有裝置,約等待5分鐘後再登入即可查看您的書籍
* 重新登入後,原帳戶中的書籍如有畫線註記和收藏將有遺失的可能。登出前,請務必先行拍照備份
* 若您有任何相關疑問請至Kobo官方網站 https://help.kobo.com/hc/zh-tw 並到頁面最下方點選“聯繫我們”