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Error Bound for Computed
Contents
Index
Nonlinear Eigenvalue Problems
Subsections
Introduction
Quadratic Eigenvalue Problems
Z. Bai, G. Sleijpen, and H. van der Vorst
Introduction
Transformation to Linear Form
Spectral Transformations for QEP
Invert QEP.
Shifted QEP.
Shift-and-Invert QEP.
QEP with Cayley Transform.
Numerical Methods for Solving Linearized Problems
Jacobi-Davidson Method
Notes and References
Higher Order Polynomial Eigenvalue Problems
Nonlinear Eigenvalue Problems with Orthogonality Constraints
R. Lippert and A. Edelman
Introduction
MATLAB Templates
Sample Problems and Their Differentials
The Procrustes Problem
Nearest-Jordan Structure
Trace Minimization
Trace Minimization with a Nonlinear Term
Simultaneous Schur Decomposition Problem
Simultaneous Diagonalization
Numerical Examples
A Sample Procrustes Problem
A Sample Jordan Block Problem
A Sample Trace Minimization Problem
A Sample LDA Toy Problem (Trace Minimization with Nonlinear Term)
A Sample Simultaneous Schur Decomposition Problem
A Sample Diagonalization Problem
Modifying the Templates
Subroutine Dependencies
Under the Hood
What to Modify
Geometric Technicalities
Manifolds
The Difference Between a Tangent and a Differential
Inner Products, Gradients, and Differentials
Getting Around
Covariant Differentiation
Inverting the Covariant Hessian (Technical Considerations)
Susan Blackford 2000-11-20
