We present an algorithm to reduce the computational complexity for plane-wave codes used in electronic structure calculations. The proposed algorithm avoids the diagonalization of large Hermitian matrices arising in such problems. The computational time for the diagonalization procedure typically grows as the cube of the number of atoms, or the number of eigenvalues required. To reduce this com...

Many numerical methods, such as tensor network approaches including density matrix renormalization group calculations, have been developed to calculate the extreme/ground states of quantum many-body systems. However, little attention has paid central states, which are exponentially close each other in terms system size. We propose a Delta-Davidson (DELDAV) method effciently find interior (inclu...

In this work, we propose a multigrid preconditioner for Jacobian-free Newton-Krylov (JFNK) methods. Our method does not require knowledge of the Jacobian at any level hierarchy. As it is common in standard methods, proposed also relies on three building blocks: transfer operators, smoothers, and coarse solver. addition to restriction prolongation operator, use projection operator current Newton...

In this paper, we present a quasi-Newton (QN) algorithm for joint independent subspace analysis (JISA). JISA is a recently proposed generalization of independent vector analysis (IVA). JISA extends classical blind source separation (BSS) to jointly resolve several BSS problems by exploiting statistical dependence between latent sources across mixtures, as well as relaxing the assumption of stat...

Krylov subspace methods for approximating the action of the matrix exponential exp(A) on a vector v are analyzed with A Hermitian and negative semidefinite. Our approach is based on approximating the exponential with the commonly employed diagonal Padé and Chebyshev rational functions, which yield a system of equations with a polynomial coefficient matrix. We derive optimality properties and er...

We present a generalized projection-based order-N method which is applicable within nonorthogonal basis sets of spatially localized orbitals. The projection to the occupied subspace of a Hamiltonian, performed by means of a Chebyshev-polynomial representation of the density operator, allows the nonvariational computation of band-structure energies, density matrices, and forces for systems with ...

We present an algorithm to reduce the computational complexity for plane-wave codes used in electronic structure calculations. Our proposed algorithm avoids the diagonalization of large Hermitian matrices arising in such problems. The computational time for the diagonalization procedure typically grows as the cube of the number of atoms, or the number of eigenvalues required. To reduce this com...

In this work we consider the numerical solution of large nonlinear eigenvalue problems that arise in thermoacoustic simulations involved in the stability analysis of large combustion devices. We briefly introduce the physical modelling that leads to a nonlinear eigenvalue problem that is solved using a nonlinear fixed point iteration scheme. Each step of this nonlinear method requires the solut...

In this paper, a numerical method for solving the Fredholm and Volterra integral equations is presented. The method is based upon the second Chebyshev wavelet approximation. The properties of the second Chebyshev wavelet are first presented and then operational matrix of integration of the second Chebyshev wavelets basis and product operation matrix of it are derived. The second Chebyshev wavel...

in this study, the problem of determining an optimal trajectory of a nonlinear injection into orbit problem with minimum time was investigated. the method was based on orthogonal polynomial approximation. this method consists of reducing the optimal control problem to a system of algebraic equations by expanding the state and control vector as chebyshev or legendre polynomials with undetermined...