%0 Generic %1 Bloch2009 %A Bloch, Jacques C. R. %A Heybrock, Simon %D 2009 %K Overlap %T A nested Krylov subspace method to compute the sign function of large complex matrices %U http://arxiv.org/abs/0912.4457 %X We present an acceleration of the well-established Krylov-Ritz methods to compute the sign function of large complex matrices, as needed in lattice QCD simulations involving the overlap Dirac operator at both zero and nonzero baryon density. Krylov-Ritz methods approximate the sign function using a projection on a Krylov subspace. To achieve a high accuracy this subspace must be taken quite large, which makes the method too costly. The new idea is to make a further projection on an even smaller, nested Krylov subspace. If additionally an intermediate preconditioning step is applied, this projection can be performed without affecting the accuracy of the approximation, and a substantial gain in efficiency is achieved for both Hermitian and non-Hermitian matrices. The numerical efficiency of the method is demonstrated on lattice configurations of sizes ranging from 4^4 to 10^4, and the new results are compared with those obtained with rational approximation methods.

@misc{Bloch2009, abstract = { We present an acceleration of the well-established Krylov-Ritz methods to compute the sign function of large complex matrices, as needed in lattice QCD simulations involving the overlap Dirac operator at both zero and nonzero baryon density. Krylov-Ritz methods approximate the sign function using a projection on a Krylov subspace. To achieve a high accuracy this subspace must be taken quite large, which makes the method too costly. The new idea is to make a further projection on an even smaller, nested Krylov subspace. If additionally an intermediate preconditioning step is applied, this projection can be performed without affecting the accuracy of the approximation, and a substantial gain in efficiency is achieved for both Hermitian and non-Hermitian matrices. The numerical efficiency of the method is demonstrated on lattice configurations of sizes ranging from 4^4 to 10^4, and the new results are compared with those obtained with rational approximation methods. }, added-at = {2009-12-23T09:16:14.000+0100}, author = {Bloch, Jacques C. R. and Heybrock, Simon}, biburl = {https://www.bibsonomy.org/bibtex/2ec54319db8799c1355f0212fc14d2d37/gber}, description = {[0912.4457] A nested Krylov subspace method to compute the sign function of large complex matrices}, interhash = {7487214bcd0f9527fcf4da257d74cf1f}, intrahash = {ec54319db8799c1355f0212fc14d2d37}, keywords = {Overlap}, note = {cite arxiv:0912.4457 Comment: 16 pages, 10 figures}, timestamp = {2009-12-23T09:16:14.000+0100}, title = {A nested Krylov subspace method to compute the sign function of large complex matrices}, url = {http://arxiv.org/abs/0912.4457}, year = 2009 }