Eigenvalue Problems: Theory, Algorithms and Applications
Outline
Overview
Standard Eigenvalue Problem
Standard Eigenvalue Problem
Properties
Properties
Properties
Properties
Special Case
Generalized Eigenvalue Problem
Generalized Eigenvalue Problem
Properties
Properties
Properties
Properties (continued)
Properties (continued)
Special Case
l-Matrix Problem
l-Matrix Problem
Equivalent Formulations
Special Case
Nonlinear Eigenvalue Problems
Resulting Sequence of Linear Problems
Algorithms
Solving Linear Eigenvalue Problems
Solving Linear Eigenvalue Problems
Solving Linear Eigenvalue Problems
Example
Reduction to Hessenberg Form
Reduction to Hessenberg Form
QR Algorithm
QR Algorithm
Triangular Systems
Triangular Systems
Back-Transformation of Eigenvectors
Back-Transformation of Eigenvectors
Full QR Algorithm
Standard Eigenproblem Solvers
Generalized Eigenproblem Solvers
l-Matrix Solvers
Applications
Application Examples
Current Research
Restricted Closed-Shell Hartree-Fock Approximation: The Roothaan Equations
Roothaan Equations
Self-Consistent-Field Procedure
SCF Procedure
Serial Eigenproblem Solver FC = C e
Serial Eigenproblem Solver FC = C e
Serial Eigenproblem Solver FC = C e
Parallel Eigenproblem Solver FC = C e
SCF Procedure
Approximate Eigenproblem FC = C e
Approximate Approximate Eigenproblem
Generalization of Divide and Conquer Algorithm