Related papers: CASSCF response equations revisited: a simple and …
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the…
Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to…
Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…
We propose an efficient algorithm for the recently published electron/hole-transfer Dynamical-weighted State-averaged Constrained CASSCF (eDSC/hDSC) method studying charge transfer states and D$_1$-D$_0$ crossings for systems with odd…
Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
The randomized Kaczmarz algorithm is one of the most popular approaches for solving large-scale linear systems due to its simplicity and efficiency. In this paper, we propose two classes of global randomized Kaczmarz methods for solving…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
When the eigenvalues of the coefficient matrix for a linear scalar ordinary differential equation are of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The…
In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…
For Hermitian positive definite linear systems and eigenvalue problems, the eigCG algorithm is a memory efficient algorithm that solves the linear system and simultaneously computes some of its eigenvalues. The algorithm is based on the…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
We present the first parallel algorithm for solving systems of linear equations in symmetric, diagonally dominant (SDD) matrices that runs in polylogarithmic time and nearly-linear work. The heart of our algorithm is a construction of a…
We report an efficient algorithm using density fitting for the relativistic complete active space self-consistent field (CASSCF) method, which is significantly more stable than the algorithm previously reported by one of the authors [J. E.…
To efficiently solve large scale nonlinear systems, we propose a novel Random Greedy Fast Block Kaczmarz method. This approach integrates the strengths of random and greedy strategies while avoiding the computationally expensive…
When a system of first order linear ordinary differential equations has eigenvalues of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The cost of representing…
Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
In symmetric block eigenvalue algorithms, such as the subspace iteration algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm, a large block size is often employed to achieve robustness and rapid…