Hydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a Brownian dynamics simulation. However, the calculation of correlated Brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studie...

Hydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a brownian dynamics simulation. However, the calculation of correlated brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studie...

A Chebyshev polynomial of a square matrix A is a monic polynomial p of specified degree that minimizes ‖p(A)‖2. The study of such polynomials is motivated by the analysis of Krylov subspace iterations in numerical linear algebra. An algorithm is presented for computing these polynomials based on reduction to a semidefinite program which is then solved by a primaldual interior point method. Exam...

In this paper, by introducing a class of relaxed filtered Krylov subspaces, we propose the subspace method for computing eigenvalues with largest real parts and corresponding eigenvectors non-symmetric matrices. As by-products, generalizations Chebyshev–Davidson solving eigenvalue problems are also presented. We give convergence analysis complex Chebyshev polynomial, which plays significant rol...

It is widely believed that Krylov subspace iterative methods are better than Chebyshev semi-iterative methods. When the solution of a linear system with a symmetric and positive definite coefficient matrix is required, the Conjugate Gradient method will compute the optimal approximate solution from the appropriate Krylov subspace, that is, it will implicitly compute the optimal polynomial. Henc...

It is shown that the four vector extrapolation methods, minimal polynomial extrapolation, reduced rank extrapolation, modified minimal polynomial extrapolation, and topological epsilon algorithm, when applied to linearly generated vector sequences, are Krylov subspace methods, and are equivalent to some well known conjugate gradient type methods. A unified recursive method that includes the con...

Solving the electronic structure problem for nanoscale systems remains a computationally challenging problem. The numerous degrees of freedom, both electronic and nuclear, make the problem impossible to solve without some effective approximations. Here we illustrate some advances in algorithm developments to solve the Kohn-Sham eigenvalue problem, i.e. we solve the electronic structure problem ...

We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with high-order filter polynomials obtained from a regularized Chebyshev expansion of a window function. After a short discussion of the conceptual foun...

in this paper, we first discuss about canonical dual of g-frameλp = {λip ∈ b(h, hi) : i ∈ i}, where λ = {λi ∈ b(h, hi) :i ∈ i} is a g-frame for a hilbert space h and p is the orthogonalprojection from h onto a closed subspace m. next, we provethat, if λ = {λi ∈ b(h, hi) : i ∈ i} and θ = {θi ∈ b(k, hi) :i ∈ i} be respective g-frames for non zero hilbert spaces hand k, and λ and θ are unitarily e...