Related papers: Schwarz Modulus Based Matrix Splittings with Minim…
The partial Schur factorization can be used to represent several eigenpairs of a matrix in a numerically robust way. Different adaptions of the Arnoldi method are often used to compute partial Schur factorizations. We propose here a…
Performing Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances, as well as estimating model hyperparameters. Although direct matrix factorizations…
To fully leverage the multi-task optimization paradigm for accelerating the solution of expensive scheduling problems, this study has effectively tackled three vital concerns. The primary issue is identifying auxiliary tasks that closely…
This article presents a class of modified new modulus-based iterative methods to process the large and sparse implicit complementarity problem (ICP). By using two positive diagonal matrices, we formulate a fixed-point equation which is…
The present article provides an efficient and accurate hybrid method to price American standard options in certain jump-diffusion models as well as American barrier-type options under the Black & Scholes framework. Our method generalizes…
A novel very simple method for finding roots of polynomials over finite fields has been proposed. The essence of the proposed method is to search the roots via nested cycles over the subgroups of the multiplicative group of the Galois…
We propose a computationally efficient Schwarz method for elliptic equations with rough media. A random sampling strategy is used to find low-rank approximations of all local solution maps in the offline stage; these maps are used to…
We consider the swelling of hydrogels as an example of a chemo-mechanical problem with strong coupling between the mechanical balance relations and the mass diffusion. The problem is cast into a minimization formulation using a…
Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank…
Software model checking is a challenging problem, and generating relevant invariants is a key factor in proving the safety properties of a program. Program invariants can be obtained by various approaches, including lightweight procedures…
We study overlapping Schwarz methods for the Helmholtz equation posed in any dimension with large, real wavenumber and smooth variable wave speed. The radiation condition is approximated by a Cartesian perfectly-matched layer (PML). The…
The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate single- as well as…
This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of…
An effective power based parallel preconditioner is proposed for general large sparse linear systems. The preconditioner combines a power series expansion method with some low-rank correction techniques, where the Sherman-Morrison-Woodbury…
When the underlying asset displays oscillations, spikes or heavy-tailed distributions, the lognormal diffusion process (for which Black and Scholes developed their momentous option pricing formula) is inadequate: in order to overcome these…
We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation…
We consider the problem of private distributed matrix multiplication under limited resources. Coded computation has been shown to be an effective solution in distributed matrix multiplication, both providing privacy against the workers and…
Nonnegative matrix factorization has been widely applied in face recognition, text mining, as well as spectral analysis. This paper proposes an alternating proximal gradient method for solving this problem. With a uniformly positive lower…
A nested Schur complement solver is proposed for iterative solution of linear systems arising in exponential and implicit time integration of the Maxwell equations with perfectly matched layer (PML) nonreflecting boundary conditions. These…
When used to accelerate the convergence of fixed-point iterative methods, such as the Picard method, which is a kind of nonlinear fixed-point iteration, polynomial extrapolation techniques can be very effective. The numerical solution of…