DocumentationParallel Solution of Large-scale Sparse Linear Eigenvalue Problems
The generalized conjugate gradient algorithm is a type of subspace projection method, which uses the block damping inverse power idea to generate triple blocks [X,P,W], where X saves the current eigenvector approximation, P saves the information from previous iteration step, and W saves vectors from X by the inverse power iteration with some CG steps. We name this method as generalized conjugate gradient algorithm since the structure of triple blocks [X,P,W] is similar to that of conjugate gradient method.
GCGE is a currently active project, we are striving to bring new improvements and new algorithms on a regular basis. Here we list the main improvements we have made.
The converged eigenpairs do not participate the subsequent iteration;
The sizes of P and W are set to be blockSize, which is equal to numEigen/5 as default;
The shift is selected dynamically when solving W;
The large scale orthogonalization to V is transformed into the small scale orthogonalization to P and a large scale orthogonalization to W;
A moving mechnism is used when computing large scale eigenvalue problem.
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