A Matlab implementation of the Implicitly Restarted Arnoldi Method for solving large-scale eigenvalue problems
Richard J. Radke · 1996
This thesis describes a Matlab implementation of the Implicitly Restarted Arnoldi Method for computing a few selected eigenvalues of large structured matrices. Shiftand -invert methods allow the calculation of the eigenvalues nearest anypointinthe complex plane, and polynomial acceleration techniques aid in computing eigenvalues of operators which are de#ned by m-#les instead of Matlab matrices. These new Matlab functions will be incorporated into the upcoming version 5 of Matlab and will greatly extend Matlab's capability to deal with manyreal-world eigenvalue problems that were intractable in version 4. The thesis begins with a discussion of the Implicitly Restarted Arnoldi Method. The bulk of the thesis is a user's manual for the Matlab functions which implement this algorithm. The user's guide not only describes the functions' syntax and structure but also discusses some of the di#culties that were overcome during their development. The thesis concludes with several examples of t...