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References in periodicals archive ?
8 with strong clustering for the optimal circulant preconditioned well-conditioned dual Toeplitz Schur complements [S.
We have to remark that for this example we get only a weak clustering and not a strong clustering for the band Toeplitz preconditioned ill-conditioned Schur complement, since the Hankel matrix related to the function x is similar to the Hilbert matrix (Theorem 3.
For the circulant preconditioned matrix for the Schur complement as well as for the block circulant preconditioned matrix for the BT system we get only a weak clustering (Theorem 3.
We get the same remarks as in the previous example except the band Toeplitz preconditioned ill-conditioned Schur complement.
This system is efficiently solved by band Toeplitz preconditioned method to get superlinear convergence.
We get superlinearity in all preconditioned methods which confirms the validity of Theorem 4.
Multigrid preconditioned gradient methods are popular for applications, e.
Preconditioned eigensolvers for such equations are analyzed in [54, 55], where, in particular, a generalization of the theory of a preconditioned subspace iteration method of [19, 20] is presented.
Let us finally highlight that in the multigrid preconditioned gradient eigensolvers we recommend, no eigenvalue problems are solved on coarse grids; thus, there are no limitations on the coarse grid size associated with approximation of eigenfunctions.
In Section 3, we describe the LOBPCG method of [33, 34, 35, 36], and a simpler, but slower, method, the block preconditioned steepest descent (BPSD), analyzed in .
We compare several preconditioned eigensolvers: PSD, LOPCG and their block versions.
For preconditioned gradient eigensolvers, it is not important whether the matrix B is diagonal; thus, a mass condensation in the finite element method (FEM) is not necessary.
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- Preconceptual Design Phase
- preconceptual stage
- Precondition Failed
- Preconditioned Conjugate Gradient
- Preconditioned conjugate gradient method
- Preconditioned Conjugate Residual
- Preconditioned Inverse Iteration
- Preconditioning Interim Operating Management Recommendation
- preconduction current
- Preconfigured Unit Loads