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A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…

Numerical Analysis · Mathematics 2016-02-23 Josef Rebenda , Zdeněk Šmarda

In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…

Machine Learning · Statistics 2022-03-31 Anatoli Juditsky , Andrei Kulunchakov , Hlib Tsyntseus

This paper presents an efficient reversible algorithm for linear regression, both with and without ridge regression. Our reversible algorithm matches the asymptotic time and space complexity of standard irreversible algorithms for this…

Data Structures and Algorithms · Computer Science 2021-12-01 Erik D. Demaine , Jayson Lynch , Jiaying Sun

We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…

Numerical Analysis · Mathematics 2023-12-13 Johannes J. Brust , Michael A. Saunders

For lossy image compression systems, we develop an algorithm, iterative refinement, to improve the decoder's reconstruction compared to standard decoding techniques. Specifically, we propose a recurrent neural network approach for…

Computer Vision and Pattern Recognition · Computer Science 2018-11-13 Alexander G. Ororbia , Ankur Mali , Jian Wu , Scott O'Connell , David Miller , C. Lee Giles

While diffusion-based image restoration (IR) methods have achieved remarkable success, they are still limited by the low inference speed attributed to the necessity of executing hundreds or even thousands of sampling steps. Existing…

Computer Vision and Pattern Recognition · Computer Science 2024-11-26 Zongsheng Yue , Jianyi Wang , Chen Change Loy

When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same…

Numerical Analysis · Mathematics 2025-01-23 Marcella Bonazzoli , Houssem Haddar , Tuan Anh Vu

The iterations of many sparse estimation algorithms are comprised of a fixed linear filter cascaded with a thresholding nonlinearity, which collectively resemble a typical neural network layer. Consequently, a lengthy sequence of algorithm…

Machine Learning · Computer Science 2016-05-11 Bo Xin , Yizhou Wang , Wen Gao , David Wipf

The aim of this paper is to present a first evaluation of a dynamic partition strategy associated to the recently proposed asynchronous distributed computation scheme based on the D-iteration approach. The D-iteration is a fluid diffusion…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-03-13 Dohy Hong

In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…

Numerical Analysis · Mathematics 2025-06-05 Dakang Cen , Wenlong Zhang , Junbin Zhong

A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work on compressed sensing, a recursive mesh refinement procedure…

Numerical Analysis · Mathematics 2009-02-26 Sadegh Jokar , Volker Mehrmann , Marc Pfetsch , Harry Yserentant

In optimal control problem, policy iteration (PI) is a powerful reinforcement learning (RL) tool used for designing optimal controller for the linear systems. However, the need for an initial stabilizing control policy significantly limits…

Optimization and Control · Mathematics 2024-11-13 Zhen Pang , Shengda Tang , Jun Cheng , Shuping He

Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…

Numerical Analysis · Mathematics 2013-11-25 Anastasia Cornelio , Federica Porta , Marco Prato , Luca Zanni

Estimation of actual errors from the residue in iterative solutions is necessary for efficient solution of large problems when their condition number is much larger than one. Such estimators for conjugate gradient algorithms used to solve…

Numerical Analysis · Mathematics 2014-06-27 Aashish Vishwakarma , Murugesan Venkatapathi

The randomized row method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple…

Numerical Analysis · Mathematics 2024-11-06 Nian-Ci Wu , Chengzhi Liu , Yatian Wang , Qian Zuo

Recent development on mixed precision techniques has largely enhanced the performance of various linear algebra solvers, one of which being the solver for the least squares problem $\min_{x}\lVert b-Ax\rVert_{2}$. By transforming least…

Numerical Analysis · Mathematics 2025-09-09 Bowen Gao , Yuxin Ma , Meiyue Shao

In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…

Numerical Analysis · Mathematics 2014-07-22 Wolfgang Erb , Evgeniya V. Semenova

In application of tomography imaging, limited-angle problem is a quite practical and important issue. In this paper, an iterative reprojection-reconstruction (IRR) algorithm using a modified Papoulis-Gerchberg (PG) iterative scheme is…

Computer Vision and Pattern Recognition · Computer Science 2019-05-01 Yuli Sun , Jinxu Tao , Conggui Liu

The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…

Optimization and Control · Mathematics 2019-09-02 Kazuhiro Hishinuma , Hideaki Iiduka

The iterative rational Krylov algorithm (\textsf{IRKA}) is a popular approach for producing locally optimal reduced-order $\mathcal{H}_2$-approximations to linear time-invariant (LTI) dynamical systems. Overall, \textsf{IRKA} has seen…

Numerical Analysis · Mathematics 2019-11-15 C. Beattie , Z. Drmac , S. Gugercin