Numerical analysts physicists and signal processing engineers have proposed algo rithms that might be called conjugate gradient for problems associated with the com putation of eigenvalues There are many variations mostly one eigenvalue at a time though sometimes block algorithms are proposed Is there a correct conjugate gradi ent algorithm for the eigenvalue problem How are the algorithms rela...

With the presence of a uniform vertical magnetic field and suspended particles, thermocapillary instability in a horizontal liquid layer is investigated. The resulting eigenvalue is solved by the Galerkin technique for various basic temperature gradients. It is found that the presence of magnetic field always has a stability effect of increasing the critical Marangoni number. Keywords—Marangoni...

We investigate eigensolvers for computing a few of the smallest eigenvalues of a generalized eigenvalue problem resulting from the finite element discretization of the time independent Maxwell equation. Various multilevel preconditioners are employed to improve the convergence and memory consumption of the JacobiDavidson algorithm and of the locally optimal block preconditioned conjugate gradie...

The iterative diagonalization of a sequence of large ill-conditioned generalized eigenvalue problems is a computational bottleneck in quantum mechanical methods employing nonorthogonal basis functions for ab initio electronic structure calculations. In this paper, we propose a hybrid preconditioning scheme to effectively combine global and locally accelerated preconditioners for rapid iterative...

Large-scale electronic structure calculations usually involve huge nonlinear eigenvalue problems. A method for solving these problems without employing expensive eigenvalue decompositions of the Fock matrix is presented in this work. The sparsity of the input and output matrices is preserved at every iteration, and the memory required by the algorithm scales linearly with the number of atoms of...

Eigenvalue and condition number estimates for preconditioned iteration matrices provide the information required to estimate the rate of convergence of iterative methods, such as preconditioned conjugate gradient methods. In recent years various estimates have been derived for (perturbed) modified (block) incomplete factorizations. We survey and extend some of these and derive new estimates. In...

Known spectral methods for graph bipartition and image segmentation require numerical solution of eigenvalue problems with the graph Laplacian. We discuss several modern preconditioned eigenvalue solvers for computing the Fiedler vectors of large scale eigenvalue problems. The ultimate goal is to find a method with a linear complexity, i.e. a method with computational costs that scale linearly ...

We study three wave function optimization methods based on energy minimization in a variational Monte Carlo framework: the Newton, linear, and perturbative methods. In the Newton method, the parameter variations are calculated from the energy gradient and Hessian, using a reduced variance statistical estimator for the latter. In the linear method, the parameter variations are found by diagonali...