ETNA - Electronic Transactions on Numerical Analysis最新文献_第8页

Modulus-based circulant and skew-circulant splitting iteration method for the linear complementarity problem with a Toeplitz matrix Toeplitz矩阵线性互补问题的模循环和斜循环分裂迭代方法

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol55s391

Min-yen Wu, Chenliang Li

引用次数: 1

A decoupling finite element method with different time steps for the micropolar fluid model 微极流体模型的不同时间步长解耦有限元方法

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol55s263

Pengzhan Huang, C. Liao

引用次数: 0

A contribution to the conditioning of the mixed least-squares scaled total least-squares problem 对混合最小二乘缩放总最小二乘问题条件的贡献

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol55s618

L. Meng

引用次数: 0

The LSQR method for solving tensor least-squares problems 求解张量最小二乘问题的LSQR方法

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol55s92

A. Bentbib, A. Khouia, H. Sadok

引用次数: 2

Exploiting compression in solving discretized linear systems 利用压缩求解离散线性系统

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol55s341

Erin Carrier, M. Heath

{"title":"Exploiting compression in solving discretized linear systems","authors":"Erin Carrier, M. Heath","doi":"10.1553/etna_vol55s341","DOIUrl":"https://doi.org/10.1553/etna_vol55s341","url":null,"abstract":"We propose a method for exploiting compression in computing the solution to a system of linear algebraic equations. The method is based on computing an approximate solution in a reduced space, and thus we seek a basis in which the solution has a compressed representation and can consequently be computed more efficiently. Although the method is completely general, it is especially effective for linear systems resulting from discretization of an underlying continuous problem, which will be our main focus. We address three primary issues: (1) how to compute an approximate solution to a given linear system using a given basis, (2) how to choose a basis that will yield significant compression, and (3) how to detect when the chosen basis is of sufficient dimension to provide a satisfactory approximation. While all three aspects have antecedents in previous ideas and methods, we combine, adapt, and extend them in a manner we believe to be novel for the purpose of solving discretized linear systems. We demonstrate that the resulting method can be competitive with—and often substantially outperforms—current standard methods and is effective for efficiently solving linear systems resulting from the discretization of major classes of continuous problems, including both differential equations and integral equations.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128317058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Upper Hessenberg and Toeplitz Bohemian matrix sequences: a note on their asymptotical eigenvalues and singular values Upper Hessenberg和Toeplitz波西米亚矩阵序列:关于它们的渐近特征值和奇异值的注记

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol55s76

M. Bogoya, S. Serra-Capizzano, K. Trotti

引用次数: 1

Decomposition and composition of deep convolutional neural networks and training acceleration via sub-network transfer learning 深度卷积神经网络的分解与组成及基于子网络迁移学习的训练加速

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol56s157

Linyan Gu, Wei Zhang, Jia Liu, X. Cai

{"title":"Decomposition and composition of deep convolutional neural networks and training acceleration via sub-network transfer learning","authors":"Linyan Gu, Wei Zhang, Jia Liu, X. Cai","doi":"10.1553/etna_vol56s157","DOIUrl":"https://doi.org/10.1553/etna_vol56s157","url":null,"abstract":"Deep convolutional neural network (DCNN) has led to significant breakthroughs in deep learning. However, larger models and larger datasets result in longer training times slowing down the development progress of deep learning. In this paper, following the idea of domain decomposition methods, we propose and study a new method to parallelize the training of DCNNs by decomposing and composing DCNNs. First, a global network is decomposed into several sub-networks by partitioning the width of the network (i.e., along the channel dimension) while keeping the depth constant. All the sub-networks are individually trained, in parallel without any interprocessor communication, with the corresponding decomposed samples from the input data. Then, following the idea of nonlinear preconditioning, we propose a sub-network transfer learning strategy in which the weights of the trained sub-networks are recomposed to initialize the global network, which is then trained to further adapt the parameters. Some theoretical analyses are provided to show the effectiveness of the sub-network transfer learning strategy. More precisely speaking, we prove that (1) the initialized global network can extract the feature maps learned by the sub-networks; (2) the initialization of the global network can provide an upper bound and a lower bound for the cost function and the classification accuracy with the corresponding values of the trained sub-networks. Some experiments are provided to evaluate the proposed methods. The results show that the sub-network transfer learning strategy can indeed provide good initialization and accelerate the training of the global network. Additionally, after further training, the transfer learning strategy shows almost no loss of accuracy and sometimes the accuracy is higher than if the network is initialized randomly.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132421329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

A computational framework for edge-preserving regularization in dynamic inverse problems 动态逆问题中保边正则化的计算框架

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol58s486

M. Pasha, A. Saibaba, S. Gazzola, Malena I. Español, E. D. Sturler

{"title":"A computational framework for edge-preserving regularization in dynamic inverse problems","authors":"M. Pasha, A. Saibaba, S. Gazzola, Malena I. Español, E. D. Sturler","doi":"10.1553/etna_vol58s486","DOIUrl":"https://doi.org/10.1553/etna_vol58s486","url":null,"abstract":". We devise efﬁcient methods for dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change in time. Our goal is to solve for all the quantities of interest simultaneously. We consider large-scale ill-posed problems made more challenging by their dynamic nature and, possibly, by the limited amount of available data per measurement step. To alleviate these difﬁculties, we apply a uniﬁed class of regularization methods that enforce simultaneous regularization in space and time (such as edge enhancement at each time instant and proximity at consecutive time instants) and achieve this with low computational cost and enhanced accuracy. More precisely, we develop iterative methods based on a majorization-minimization (MM) strategy with quadratic tangent majorant, which allows the resulting least-squares problem with a total variation regularization term to be solved with a generalized Krylov subspace (GKS) method; the regularization parameter can be determined automatically and efﬁciently at each iteration. Numerical examples from a wide range of applications, such as limited-angle computerized tomography (CT), space-time image deblurring, and photoacoustic tomography (PAT), illustrate the effectiveness of the described approaches.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127936560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Conformal modulus and planar domains with strong singularities and cusps 保角模与强奇异点与尖点的平面域

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/ETNA_VOL48S462

H. Hakula, A. Rasila, M. Vuorinen

引用次数: 11

On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots 一种精确计算所有多项式根的补偿Ehrlich-Aberth方法

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol55s401

T. R. Cameron, S. Graillat

引用次数: 1