Basis selection in LOBPCG
The purpose of our paper is to discuss basis selection for Knyazevs locally optimal block preconditioned conjugate gradient (LOBPCG) method. An inappropriate choice of basis can lead to ill-conditioned Gram matrices in the RayleighRitz analysis that can delay convergence or produce inaccurate eigenpairs. We demonstrate that the choice of basis is not merely related to computing in finite precision arithmetic. We propose a representation that maintains orthogonality of the basis vectors and so has excellent numerical properties.
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