Results

**11 - 20**of**20**### BUHEP-07-07 Strange quark contribution to nucleon form factors

, 2007

"... We discuss methods for the calculation of disconnected diagrams and their application to various form factors of the nucleon. In particular, we present preliminary results for the strange contribution to the scalar and axial form factors, calculated with Nf = 2 dynamical flavors of Wilson fermions o ..."

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We discuss methods for the calculation of disconnected diagrams and their application to various form factors of the nucleon. In particular, we present preliminary results for the strange contribution to the scalar and axial form factors, calculated with Nf = 2 dynamical flavors of Wilson fermions on an anisotropic lattice. The XXV International Symposium on Lattice Field Theory

### Optimization of the deflated Conjugate Gradient algorithm for the solving of elliptic equations on massively parallel machines

, 2012

"... 1.1 State-of-the-art and motivation................................ 3 ..."

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### Deflated Hermitian Lanczos Methods for Multiple

"... A deflated and restarted Lanczos algorithm to solve hermitian linear systems, and at the same time compute eigenvalues and eigenvectors for application to multiple right-hand sides, is de-scribed. For the first right-hand side, eigenvectors with small eigenvalues are computed while simultaneously so ..."

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A deflated and restarted Lanczos algorithm to solve hermitian linear systems, and at the same time compute eigenvalues and eigenvectors for application to multiple right-hand sides, is de-scribed. For the first right-hand side, eigenvectors with small eigenvalues are computed while simultaneously solving the linear system. Two versions of this algorithm are given. The first is called Lan-DR and is based on conjugate gradient (CG) implementation of the Lanczos algorithm. This version will be optimal for the hermitian positive definite case. The second version is called MinRes-DR and is based on the minimum residual (MinRes) implementation of Lanczos algo-rithm. This version is optimal for indefinite hermitian systems where the CG algorithm is subject to instabilities. For additional right-hand sides, we project over the calculated eigenvectors to speed up convergence. The algorithms used for subsequent right-hand sides are called D-CG and D-MinRes respectively. After some introductory examples are given, we show tests for the case of Wilson fermions at kappa critical. A considerable speed up in the convergence is observed compared to unmodified CG and MinRes.

### The XXV International Symposium on Lattice Field Theory

, 2007

"... We discuss methods for the calculation of disconnected diagrams and their application to various form factors of the nucleon. In particular, we present preliminary results for the strange contri-bution to the scalar and axial form factors, calculated with N f = 2 dynamical flavors of Wilson fermions ..."

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We discuss methods for the calculation of disconnected diagrams and their application to various form factors of the nucleon. In particular, we present preliminary results for the strange contri-bution to the scalar and axial form factors, calculated with N f = 2 dynamical flavors of Wilson fermions on an anisotropic lattice.

### POLYNOMIAL PRECONDITIONED GMRES AND GMRES-DR

"... We look at solving large nonsymmetric systems of linear equations using polynomial preconditioned Krylov methods. We give a simple way to find the polynomial. It is shown that polynomial preconditioning can significantly improve restarted GMRES for difficult problems, and the reasons for this are ex ..."

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We look at solving large nonsymmetric systems of linear equations using polynomial preconditioned Krylov methods. We give a simple way to find the polynomial. It is shown that polynomial preconditioning can significantly improve restarted GMRES for difficult problems, and the reasons for this are examined. Stability is discussed and algorithms are given for increased stability. Next we apply polynomial preconditioning to GMRES with deflated restarting. It is shown that this is worthwhile for sparse matrices and for problems with many small eigenvalues. Multiple right-hand sides are also considered.

### am Fachbereich Mathematik der

"... Krylov subspace methods for shifted unitary matrices and eigenvalue deflation ..."

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Krylov subspace methods for shifted unitary matrices and eigenvalue deflation