A Generalized Lanczos Method for Solving Large Skew-symmetric Eigenproblems
|Keywords||Skew-symmetric matrices The Generalized Lanczos process Interior eigenvalue Refine projection Refine vector Harmonic projection Harmoic ritz value Harmoic ritz vector|
This paper investigates the solution of large scale skew symmetric eigenvalue problems using generalized Lanczos methods. It consists of four chapters.Chapter one gives a background of large eigenvalue problems, the main methods for solving them. The state of the art of the area is reviewed briefly. The work of the thesis is outlined.In Chapter two, we recall the Lanczos algorithm, the properties of the skew symmetric matrix, and the Jacobi iteration method for solving skew matrix eigenvalue problems.In Chapter three, we present the generalized Lanczos method and its refined variant for solving large scale skew symmetric eigenvalue problems.In Chapter four, the harmonic generalized Lanczos method is investigated, which is more suitable for computing eigenvalues in the interior of the spectrum.