Research on Eigenvalue Computations

Given a matrix Α, the eigenvalue λ and eigenvector x satisfy the equation Αx = λx. For a small matrix, the eigenvalues and eigenvectors can be computed using LAPACK. The methods used in LAPACK are generally based on QR factorizations and similar type of factorizations. For large or sparse matrices, or for problems that only seek to compute a few eigenvalues (and eigenvectors), another class of methods, generally known as "iterative methods" are more appropriate. Some of the well-known examples of iterative methods include Lanczos method, Arnoldi method and Davidson method.

TRLan software

TRLan implements the Thick-Restart Lanczos method for solving large symmetric eigenvalue problems: [Source Code in Fortran 90] [TRLan user guide (in postscript) (in PDF) (in HTML)]
nu-TRLan implements the Thick-Restart Lanczos method for solving Hermitian eigenvalue problems with an improved restarting strategy: ACM TOMS 37:3 [Source code in C] [nu-TRLan user guide]

Publications

Here is a list of publications on eigenvalue computations, and here is a list of elier work on scientific computing and related applications.

Applications using TRLan: Berkeley Segmentation Engine
Paper citing TRLan: Quantum vibrational polarons: Crystalline acetanilide revisited (2006); Self-consistent-field calculations using Chebyshev-filtered subspace iterations (2006); Single-site entanglement at the superconductor-insulator transition in the Hirsch model (2006); On c = 1 critical phases in anisotropic spin-1 chains (2004); Synthesizing Sounds from Rigid-Body Simulations (2002); Modal Analysis for Real-Time Viscoelastic Deformation (2002); Citation search results on the SIMAX paper from Google scholar; Citation search results on TRLan User Guide from Google scholar; Citation search results from MS Libra
More research work by John Wu: Bitmap Index; Connected Component Labeling; Eigenvalue Computation
Information available elsewhere on the web: CiteSeer; DBLP; Google Scholar