相关论文: Iterative solutions to the steady state density ma…
We present a technique for the approximation of a class of Hilbert space-valued maps which arise within the framework of Model Order Reduction for parametric partial differential equations, whose solution map has a meromorphic structure.…
Many scientific and engineering challenges can be formulated as optimization problems which are constrained by partial differential equations (PDEs). These include inverse problems, control problems, and design problems. As a major…
This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere. In order to achieve robust convergence behavior in the…
Presented here is a matrix inversion method utilizing quantum searching algorithm. In this method, huge Hilbert space as a whole spanned by myriad of eigen states is searched and evaluated efficiently by sequential reduction in dimension…
Sparse recovery principles play an important role in solving many nonlinear ill-posed inverse problems. We investigate a variational framework with support Oracle for compressed sensing sparse reconstructions, where the available…
Quantum state tomography is an essential component of modern quantum technology. In application to continuous-variable harmonic-oscilator systems, such as the electromagnetic field, existing tomography methods typically reconstruct the…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
We present a protocol that allows the estimation of any density matrix element for continuous-variable quantum states, without resorting to the complete reconstruction of the full density matrix. The algorithm adaptatively discretizes the…
Preconditioning for overdetermined least-squares problems has received comparatively little attention, and designing methods that are both effective and memory-efficient remains challenging. We propose a class of ILU-based preconditioners…
Can linear systems be solved faster than matrix multiplication? While there has been remarkable progress for the special cases of graph structured linear systems, in the general setting, the bit complexity of solving an $n \times n$ linear…
Least squares method is one of the simplest and most popular techniques applied in data fitting, imaging processing and high dimension data analysis. The classic methods like QR and SVD decomposition for solving least squares problems has a…
This paper studies the solution of nonsymmetric linear systems by preconditioned Krylov methods based on the normal equations, LSQR in particular. On some examples, preconditioned LSQR is seen to produce errors many orders of magnitude…
Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…
PDE-constrained optimization problems with control or state constraints are challenging from an analytical as well as numerical perspective. The combination of these constraints with a sparsity-promoting $\rm L^1$ term within the objective…
Given a zero-dimensional ideal I in K[x1,...,xn] of degree D, the transformation of the ordering of its Groebner basis from DRL to LEX is a key step in polynomial system solving and turns out to be the bottleneck of the whole solving…
We address the non-convex optimisation problem of finding a sparse matrix on the Stiefel manifold (matrices with mutually orthogonal columns of unit length) that maximises (or minimises) a quadratic objective function. Optimisation problems…
Estimating optical flows is one of the most interesting problems in computer vision, which estimates the essential information about pixel-wise displacements between two consecutive images. This work introduces an efficient dual…
In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…
In this paper, we propose a new framework for solving state estimation problems with an additional sparsity-promoting $L_1$-regularizer term. We first formulate such problems as minimization of the sum of linear or nonlinear quadratic error…
This work presents a scalable control framework based on nonlinear Model Predictive Control for high-dimensional dynamical systems. The proposed approach addresses the key challenges of model scalability and partial observability by…