Research Article
Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems
Algorithm 3
DACG-Newton algorithm.
INPUT: Matrix ; | number of sought eigenpairs ; | tolerance and maximum number of its for the outer iteration: , ITMAX; | tolerance for the initial eigenvector guess ; | tolerance and maximum number of its for the inner iteration: . | ITMAX; | parameters for the RFSAI preconditioner, | , nband, for the 1st FSAI factor and, | for the 2nd factor; | maximum allowed rank-two update in the BFGS preconditioner: . | . | Compute , an RFSAI preconditioner for , | for to | (1) Choose such that ; | (2) Compute , an approximation to by the DACG procedure with initial | vector , preconditioner and tolerance ; | (3) , ; | (4) while and do | (1) . | (2) Solve for by the PCG method with preconditioner and tolerance . | (3) , . | (4) MOD ; . | (5) | (6) end while | (7) Assume and . Set | end for |
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