Table of ContentsEigenvalue 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 |
Author: Robert C. Ward |