Related papers: Preconditioned nonlinear conjugate gradient method…
We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-optimize framework that integrates finite element…
We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…
We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in.…
The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit…
The conjugate gradient (CG) method, a standard and vital way of minimizing the energy of a variational state, is applied to solve several problems in Skyrmion physics. The single-Skyrmion profile optimizing the energy of a two-dimensional…
This paper presents the sparsifying preconditioner for the time-harmonic Maxwell's equations in the integral formulation. Following the work on sparsifying preconditioner for the Lippmann-Schwinger equation, this paper generalizes that…
The Stokes system with constant viscosity can be cast into different formulations by exploiting the incompressibility constraint. For instance the strain in the weak formulation can be replaced by the gradient to decouple the velocity…
The nonlinear conjugate gradient methods are known to be an effective approach for standard unconstrained optimization problems especially for large-scale problems. This paper proposes a proximal nonlinear conjugate gradient method, which…
We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…
This paper proposes a matrix-free residual evaluation technique for the hybridizable discontinuous Galerkin method requiring a number of operations scaling only linearly with the number of degrees of freedom. The method results from…
We present the open source micromagnetic framework, MagTense, which utilizes a novel discretization approach of rectangular cuboid or tetrahedron geometry "tiles" to analytically calculate the demagnetization field. Each tile is assumed to…
This paper provides the first provable $\mathcal{O}(N \log N)$ algorithms for the linear system arising from the direct finite element discretization of the fourth-order equation with different boundary conditions on unstructured grids of…
Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…
Convex relaxation methods are powerful tools for studying the lowest energy of many-body problems. By relaxing the representability conditions for marginals to a set of local constraints, along with a global semidefinite constraint, a…
We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize approach applied to optimal control problems constrained by a partial…
Ensembles of variational data assimilations (EDA) require solving systems of linear equations with iterative methods. The solution process can be accelerated using a limited memory preconditioner constructed with approximations of the…
The iterative diagonalization of a sequence of large ill-conditioned generalized eigenvalue problems is a computational bottleneck in quantum mechanical methods employing a nonorthogonal basis for {\em ab initio} electronic structure…
A two-step preconditioned iterative method based on the Hermitian/Skew-Hermitian splitting is applied to the solution of nonsymmetric linear systems arising from the Finite Element approximation of convection-diffusion equations. The…
We make distributed stochastic gradient descent faster by exchanging sparse updates instead of dense updates. Gradient updates are positively skewed as most updates are near zero, so we map the 99% smallest updates (by absolute value) to…
Alternating least squares (ALS) is often considered the workhorse algorithm for computing the rank-R canonical tensor approximation, but for certain problems its convergence can be very slow. The nonlinear conjugate gradient (NCG) method…