Parallel homotopy algorithm for symmetric large sparse eigenproblems

Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems

In this paper we propose a parallel preconditioner for the Newton method in the computation of the leftmost eigenpairs of large and sparse symmetric positive definite matrices. A sequence of preconditioners starting from an enhanced approximate inverse RFSAI [13] and enriched by a BFGS-like update formula is proposed to accelerate the Preconditioned Conjugate Gradient solution of the linearized...

A Chebyshev-Davidson Algorithm for Large Symmetric Eigenproblems

A polynomial filtered Davidson-type algorithm is proposed for symmetric eigenproblems, in which the correction-equation of the Davidson approach is replaced by a polynomial filtering step. The new approach has better global convergence and robustness properties when compared with standard Davidson-type methods. The typical filter used in this paper is based on Chebyshev polynomials. The goal of...

Parallel Homotopy Algorithm for Large Sparse Generalized Eigenvalue Problems: Application to Hydrodynamic Stability Analysis

A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems

An \industrial strength" algorithm for solving sparse symmetric generalized eigenproblems is described. The algorithm has its foundations in known techniques in solving sparse symmetric eigenproblems, notably the spectral transformation of Ericsson and Ruhe and the block Lanczos algorithm. However, the combination of these two techniques is not trivial; there are many pitfalls awaiting the unwa...

Parallel Sparse Linear Algebra for Homotopy Methods

Globally convergent homotopy methods are used to solve difficult nonlinear systems of equations by tracking the zero curve of a homotopy map. Homotopy curve tracking involves solving a sequence of linear systems, which often vary greatly in difficulty. In this research, a popular iterative solution tool, GMRES(k), is adapted to deal with the sequence of such systems. The proposed adaptive strat...