| FindBook |
|
有 1 項符合
凱瑟琳·史瑞伯的圖書 |
 |
$ 303 | 非線性特徵值問題--牛頓型方法與非線性瑞利函數(英文)
作者：（德）凱瑟琳·史瑞伯 出版社：哈爾濱工業大學出版社 出版日期：2021-07-01 語言：簡體中文 規格：平裝 / 193頁 / 13 x 19 x 1 cm / 普通級/ 1-1  博客來 - 數學
- 來源網頁  看圖書介紹
|
|
|
圖書介紹 - 資料來源：博客來 評分：
圖書名稱：非線性特徵值問題--牛頓型方法與非線性瑞利函數(英文)
內容簡介
本書考慮了最一般的非線性特徵值問題，而沒有對結構或譜進行假設。該書首先提供了有關簡單特徵值和奇異值分解的逆運算元表示條件的基本事實；其次研究了非線性複對稱特徵值問題的特例，給出了複對稱瑞利函數的適當定義，該定義用於匯出局部三次收斂的複對稱瑞利函數的反覆運算，以及複對稱剩餘逆反覆運算方法，制定了複對稱雅可比—大衛森算法，並進行了數值測試；最後還介紹了一種用於計算左右特徵向量的方法的加速收斂技術，並以R階代表了收斂改進。
目錄
1 Introduction
1．1 Motivation I
1．2 The Nonlinear Eigenvalue Problem
1．3 Variational Principles
1．4 Outline
1．5 Motivation II
2 Preliminaries and Basic Results
2．1 Basic Properties
2．2 Assumptions
2．2．1 Real-valued Problems
2．2．2 Complex-valued Problems
2．3 Eigenvalue Condition Numbers
2．4 Representation of the Inverse Operator
2．5 Angles and Distances
3 Nonlinear Rayleigh Functionals
3．1 Introduction and Historical Review
3．2 Existence and Stationarity of the Generalized Rayleigh Functional
3．2．1 Real-valued Problems
3．2．2 Complex-valued Problems
3．3 The Standard Nonlinear Rayleigh Functional
3．3．1 Structured Problems
3．3．2 General Problems
3．3．3 Perturbation Expansion
3．4 Generalized Quotient vs． Functional
3．4．1 Two-sided Quotient and Functional
3．4．2 One-sided Quotient and Functional
3．5 Conclusion
4 Newton-type Methods
4．1 Methods for Approximating One Eigenpair
4．2 Methods for Approximating One Eigentriple
4．2．1 Two-sided Rayleigh Functional lteration
4．2．2 Two-sided Residual Inverse Iteration
4．2．3 Alternating Rayleigh Functional Iteration
4．2．4 Generalized Rayleigh Functional Iteration
4．3 Theoretical Comparison of the Methods
4．4 Computation of the Rayleigh Functional
4．5 Numerical Experiments
4．6 Conclusion
5 Half-step Methods
6 Jacobi-Davidson-type Methods
7 Nonlinear Complex Symmetric Jacobi-Davidson
8 Summary and Outlook
編輯手記
1．1 Motivation I
1．2 The Nonlinear Eigenvalue Problem
1．3 Variational Principles
1．4 Outline
1．5 Motivation II
2 Preliminaries and Basic Results
2．1 Basic Properties
2．2 Assumptions
2．2．1 Real-valued Problems
2．2．2 Complex-valued Problems
2．3 Eigenvalue Condition Numbers
2．4 Representation of the Inverse Operator
2．5 Angles and Distances
3 Nonlinear Rayleigh Functionals
3．1 Introduction and Historical Review
3．2 Existence and Stationarity of the Generalized Rayleigh Functional
3．2．1 Real-valued Problems
3．2．2 Complex-valued Problems
3．3 The Standard Nonlinear Rayleigh Functional
3．3．1 Structured Problems
3．3．2 General Problems
3．3．3 Perturbation Expansion
3．4 Generalized Quotient vs． Functional
3．4．1 Two-sided Quotient and Functional
3．4．2 One-sided Quotient and Functional
3．5 Conclusion
4 Newton-type Methods
4．1 Methods for Approximating One Eigenpair
4．2 Methods for Approximating One Eigentriple
4．2．1 Two-sided Rayleigh Functional lteration
4．2．2 Two-sided Residual Inverse Iteration
4．2．3 Alternating Rayleigh Functional Iteration
4．2．4 Generalized Rayleigh Functional Iteration
4．3 Theoretical Comparison of the Methods
4．4 Computation of the Rayleigh Functional
4．5 Numerical Experiments
4．6 Conclusion
5 Half-step Methods
6 Jacobi-Davidson-type Methods
7 Nonlinear Complex Symmetric Jacobi-Davidson
8 Summary and Outlook
編輯手記
|
