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This paper provides a comprehensive and detailed analysis of the local convergence behavior of an extended variation of the locally optimal preconditioned conjugate gradient method (LOBPCG) for computing the extreme eigenvalue of a…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…
In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual regularized IPM, suitable for solving linearly constrained…
We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalization of matrices of dimension N…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…
This paper is concerned with the convergence analysis of an extended variation of the locally optimal preconditioned conjugate gradient method (LOBPCG) for the extreme eigenvalue of a Hermitian matrix polynomial which admits some extended…
In one of the most important methods in Density Functional Theory - the Full-Potential Linearized Augmented Plane Wave (FLAPW) method - dense generalized eigenproblems are organized in long sequences. Moreover each eigenproblem is strongly…
In the past few years, the problem of distributed consensus has received a lot of attention, particularly in the framework of ad hoc sensor networks. Most methods proposed in the literature address the consensus averaging problem by…
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering…
The adaptive $s$-step CG algorithm is a solver for sparse, symmetric positive definite linear systems designed to reduce the synchronization cost per iteration while still achieving a user-specified accuracy requirement. In this work, we…
We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the…
Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…
We introduce an adaptive finite element scheme for the efficient approximation of a (large) collection of eigenpairs of selfadjoint elliptic operators in which the adaptive refinement is driven by the solution of a single source problem --…
This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…
We carry Chebyshev-polynomial expansion of the inverse localization length of Hermitian and non-Hermitian random chains as function of energy. For Hermitian models, the expansion produces numerically this energy-dependent function in one…
This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…
This paper proposes an efficient method for computing selected generalized eigenpairs of a sparse Hermitian definite matrix pencil $(A,B)$. Based on Zolotarev's best rational function approximations of the signum function and conformal…
In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…