Related papers: Approximate Generalized Inverses with Iterative Re…
This study proposes an intrusive projection-based model-order reduction framework for nonlinear problems with a polynomial structure, solved iteratively using a Newton solver in the reduced space. It is demonstrated that for the targeted…
It is well known that for singular inconsistent range-symmetric linear systems, the generalized minimal residual (GMRES) method determines a least squares solution without breakdown. The reached least squares solution may be or not be the…
Due to its significance in terms of wave phenomena a considerable effort has been put into the design of preconditioners for the Helmholtz equation. One option to derive a preconditioner is to apply a multigrid method on a shifted operator.…
Analogues of the conjugate gradient method, MINRES, and GMRES are derived for solving boundary value problems (BVPs) involving second-order differential operators. Two challenges arise: imposing the boundary conditions on the solution while…
We mainly analyze and solve the overfitting problem of deep image prior (DIP). Deep image prior can solve inverse problems such as super-resolution, inpainting and denoising. The main advantage of DIP over other deep learning approaches is…
We introduce a new preconditioner for a recently developed pressure-robust hybridized discontinuous Galerkin (HDG) finite element discretization of the Stokes equations. A feature of HDG methods is the straightforward elimination of…
The sequential fully implicit (SFI) scheme was introduced (Jenny et al. 2006) for solving coupled flow and transport problems. Each time step for SFI consists of an outer loop, in which there are inner Newton loops to implicitly and…
We present a new deep learning paradigm for the generation of sparse approximate inverse (SPAI) preconditioners for matrix systems arising from the mesh-based discretization of elliptic differential operators. Our approach is based upon the…
In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…
This paper introduces a weighted generalized inverse framework for Fourier extensions, designed to suppress spurious oscillations in the extended region while maintaining high approximation accuracy on the original interval. By formulating…
The geometric iterative method (GIM) is widely used in data interpolation/fitting, but its slow convergence affects the computational efficiency. Recently, much work was done to guarantee the acceleration of GIM in the literature. In this…
Recent studies have shown that proximal gradient (PG) method and accelerated gradient method (APG) with restarting can enjoy a linear convergence under a weaker condition than strong convexity, namely a quadratic growth condition (QGC).…
We consider using the preconditioned-Krylov subspace method to solve the system of linear equations with a three-by-three block structure. By making use of the three-by-three block structure, eight inexact block factorization…
High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a conservation law solution and align elements of the…
We extend the operator preconditioning framework [R. Hiptmair, Comput. Math. with Appl. 52 (2006), pp.~699--706] to Petrov-Galerkin methods while accounting for parameter-dependent perturbations of both variational forms and their…
Many engineering problems involve solving large linear systems of equations. Conjugate gradient (CG) is one of the most popular iterative methods for solving such systems. However, CG typically requires a good preconditioner to speed up…
We propose an unconditionally robust and highly effective preconditioner for general symmetric positive definite (SPD) matrices based on structured incomplete factorization (SIF), called enhanced SIF (eSIF) preconditioner. The original SIF…
We introduce the Generalized Preconditioned Locally Harmonic Residual (GPLHR) method for solving standard and generalized non-Hermitian eigenproblems. The method is particularly useful for computing a subset of eigenvalues, and their eigen-…
One of the most computationally expensive steps of the low-rank ADI method for large-scale Lyapunov equations is the solution of a shifted linear system at each iteration. We propose the use of the extended Krylov subspace method for this…
High frequency integral equation methodologies display the capability of reproducing single-scattering returns in frequency-independent computational times and employ a Neumann series formulation to handle multiple-scattering effects. This…