arXiv subjects

Qinmeng Zou

Publications and source records attributed to Qinmeng Zou.

13 recordsLinked to original sources

arXiv2023

Asynchronous iterations of HSS method for non-Hermitian linear systems

A general asynchronous alternating iterative model is designed, for which convergence is theoretically ensured both under classical spectral radius bound and, then, for a classical class of matrix splittings for $\mathsf H$-matrices. The computational model can be thought of as a two-stage alternating iterative method, which well suits to the well-known Hermitian and skew-Hermitian splitting (HSS) approach, with the particularity here of considering only one inner iteration. Experimental parallel performance comparison is conducted between the generalized minimal residual (GMRES) algorithm, the standard HSS and our asynchronous variant, on both real and complex non-Hermitian linear systems respectively arising from convection-diffusion and structural dynamics problems. A significant gain on execution time is observed in both cases.

math.NA↗

arXiv2023

GMRES algorithms over 35 years

This paper is about GMRES algorithms for the solution of nonsingular linear systems. We first consider basic algorithms and study their convergence. We then focus on acceleration strategies and parallel algorithms that are useful for solving challenging systems. We also briefly discuss other problems, such as systems with multiple right-hand sides, shifted systems, and singular systems.

math.NA↗

arXiv2019

On Extensions of Limited Memory Steepest Descent Method

We present some extensions to the limited memory steepest descent method based on spectral properties and cyclic iterations. Our aim is to show that it is possible to combine sweep and delayed strategies for improving the performance of gradient methods. Numerical results are reported which indicate that our new methods are better than the original version. Some remarks on the stability and parallel implementation are shown in the end.

math.NA↗

arXiv2019

Recent Developments in Iterative Methods for Reducing Synchronization

On modern parallel architectures, the cost of synchronization among processors can often dominate the cost of floating-point computation. Several modifications of the existing methods have been proposed in order to keep the communication cost as low as possible. This paper aims at providing a brief overview of recent advances in parallel iterative methods for solving large-scale problems. We refer the reader to the related references for more details on the derivation, implementation, performance, and analysis of these techniques.

cs.DC↗

arXiv2019

Fast Gradient Methods with Alignment for Symmetric Linear Systems without Using Cauchy Step

The performance of gradient methods has been considerably improved by the introduction of delayed parameters. After two and a half decades, the revealing of second-order information has recently given rise to the Cauchy-based methods with alignment, which reduce asymptotically the search spaces in smaller and smaller dimensions. They are generally considered as the state of the art of gradient methods. This paper reveals the spectral properties of minimal gradient and asymptotically optimal steps, and then suggests three fast methods with alignment without using the Cauchy step. The convergence results are provided, and numerical experiments show that the new methods provide competitive and more stable alternatives to the classical Cauchy-based methods. In particular, alignment gradient methods present advantages over the Krylov subspace methods in some situations, which makes them attractive in practice.

math.NA↗

arXiv2019

Asynchronous Time-Parallel Method based on Laplace Transform

Laplace transform method has proved to be very efficient and easy to parallelize for the solution of time-dependent problems. However, the synchronization delay among processors implies an upper bound on the expectable acceleration factor, which leads to a lot of wasted time. In this paper, we propose an original asynchronous Laplace transform method formalized for quasilinear problems based on the well-known Gaver-Stehfest algorithm. Parallel experiments show the convergence of our new method, as well as several interesting properties compared with the classical algorithms.

cs.DC↗

arXiv2019

Parameter Estimation in the Hermitian and Skew-Hermitian Splitting Method Using Gradient Iterations

This paper presents enhancement strategies for the Hermitian and skew-Hermitian splitting method based on gradient iterations. The spectral properties are exploited for the parameter estimation, often resulting in a better convergence. In particular, steepest descent with early stopping can generate a rough estimate of the optimal parameter. This is better than an arbitrary choice since the latter often causes stability problems or slow convergence. Additionally, lagged gradient methods are considered as inner solvers for the splitting method. Experiments show that they are competitive with conjugate gradient in low precision.

math.NA↗

arXiv2019

A Novel Contactless Human Machine Interface based on Machine Learning

This paper describes a global framework that enables contactless human machine interaction using computer vision and machine learning techniques. The main originality of our framework is that only a very simple image acquisition device, as a computer camera, is sufficient to establish a rich human machine interaction as traditional devices such as mouse or keyboard. This framework is based on well known computer vision techniques and efficient machine learning techniques are used to detect and track user hand gestures so the end user can control his computer using virtual interfaces with very simple gestures.

cs.HC↗

arXiv2019

GPU Accelerated Contactless Human Machine Interface for Driving Car

In this paper we present an original contactless human machine interface for driving car. The proposed framework is based on the image sent by a simple camera device, which is then processed by various computer vision algorithms. These algorithms allow the isolation of the user's hand on the camera frame and translate its movements into orders sent to the computer in a real time process. The optimization of the implemented algorithms on graphics processing unit leads to real time interaction between the user, the computer and the machine. The user can easily modify or create the interfaces displayed by the proposed framework to fit his personnel needs. A contactless driving car interface is here produced to illustrate the principle of our framework.

cs.HC↗

arXiv2019

Asynchronous Parareal Algorithm Applied to European Option Pricing

Asynchronous iterations arise naturally in parallel computing if one wants to solve large problems with a minimization of the idle times. This paper presents an original model of asynchronous iterations for a time-domain decomposition method, namely the parareal method. The asynchronous parareal algorithm is here applied to European option pricing, and numerical experiments performed on a parallel supercomputer, illustrate the performance and efficiency of this new method.

cs.DC↗

arXiv2019

Asynchronous Communications Library for the Parallel-in-Time Solution of Black-Scholes Equation

The advent of asynchronous iterative scheme gives high efficiency to numerical computations. However, it is generally difficult to handle the problems of resource management and convergence detection. This paper uses JACK2, an asynchronous communication kernel library for iterative algorithms, to implement both classical and asynchronous parareal algorithms, especially the latter. We illustrate the measures whereby one can tackle the problems above elegantly for the time-dependent case. Finally, experiments are presented to prove the availability and efficiency of such application.

cs.DC↗

arXiv2019

A New Cyclic Gradient Method Adapted to Large-Scale Linear Systems

This paper proposes a new gradient method to solve the large-scale problems. Theoretical analysis shows that the new method has finite termination property for two dimensions and converges R-linearly for any dimensions. Experimental results illustrate first the issue of parallel implementation. Then, the solution of a large-scale problem shows that the new method is better than the others, even competitive with the conjugate gradient method.

math.NA↗

arXiv2019

Convergence Detection of Asynchronous Iterations based on Modified Recursive Doubling

This paper addresses the distributed convergence detection problem in asynchronous iterations. A modified recursive doubling algorithm is investigated in order to adapt to the non-power-of-two case. Some convergence detection algorithms are illustrated based on the reduction operation. Finally, a concluding discussion about the implementation and the applicability is presented.

cs.DC↗