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An Accelerated Conjugate Gradient Algorithm to Compute Low-Lying Eigenvalues --- a Study for the Dirac Operator in SU(2) Lattice QCD
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abstract
The low-lying eigenvalues of a (sparse) hermitian matrix can be computed with controlled numerical errors by a conjugate gradient (CG) method. This CG algorithm is accelerated by alternating it with exact diagonalisations in the subspace spanned by the numerically computed eigenvectors. We study this combined algorithm in case of the Dirac operator with (dynamical) Wilson fermions in four-dimensional $\SUtwo$ gauge fields. The algorithm is numerically very stable and can be parallelized in an efficient way. On lattices of sizes $4^4-16^4$ an acceleration of the pure CG method by a factor of~$4-8$ is found.
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Eigenspectra of Minimally Doubled Fermions
Numerical spectral flow and modified chirality operators show that Karsten-Wilczek and Borici-Creutz minimally doubled fermions satisfy the index theorem on an 8^4 SU(3) lattice with Q_top = -2.
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