非線性特徵值問題--牛頓型方法與非線性瑞利函數(英文)

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
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