Electronic Transactions on Numerical Analysis最新文献

Parameter-free restoration of piecewise smooth images 分段平滑图像的无参数恢复

4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2023-01-01 DOI: 10.1553/etna_vol59s202

Alessandro Lanza, Monica Pragliola, Fiorella Sgallari

{"title":"Parameter-free restoration of piecewise smooth images","authors":"Alessandro Lanza, Monica Pragliola, Fiorella Sgallari","doi":"10.1553/etna_vol59s202","DOIUrl":"https://doi.org/10.1553/etna_vol59s202","url":null,"abstract":"We propose a novel strategy for the automatic estimation of the two regularization parameters arising in the image decomposition variational model employed for the restoration task when the underlying corrupting noise is known to be additive white Gaussian. In the model of interest, the target image is decomposed in its piecewise constant and smooth components, with a total variation term penalizing the former and a Tikhonov term acting on the latter. The proposed criterion, which relies on the whiteness property of the noise, extends the residual whiteness principle, originally introduced in the case of a single regularization parameter. The structure of the considered decomposition model allows for an efficient estimation of the pair of unknown parameters, that can be automatically adjusted along the iterations with the alternating direction method of multipliers employed for the numerical solution. The proposed multi-parameter residual whiteness principle is tested on different images with different levels of corruption. The performed tests highlight that the whiteness criterion is particularly effective and robust when moving from a single-parameter to a multi-parameter scenario.","PeriodicalId":50536,"journal":{"name":"Electronic Transactions on Numerical Analysis","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135261969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Gauss-Laguerre approach for the resolvent of fractional powers 分数次幂解的高斯-拉盖尔方法

4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2023-01-01 DOI: 10.1553/etna_vol58s517

Eleonora Denich, Laura Grazia Dolce, Paolo Novati

引用次数: 0

Deautoconvolution in the two-dimensional case 二维情况下的反自卷积

4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2023-01-01 DOI: 10.1553/etna_vol59s24

Yu Deng, Bernd Hofmann, Frank Werner

引用次数: 1

A note on “Error bounds of Gaussian quadrature formulae with Legendre weight function for analytic integrands” by M. M. Spalević et al. M. M. spaleviki等人关于“解析积分的带Legendre权函数高斯正交公式的误差界”的注记。

4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2023-01-01 DOI: 10.1553/etna_vol59s89

Aleksandar V. Pejčev

引用次数: 1

On the numerical solution of an elliptic problem with nonlocal boundary conditions 非局部边界条件下椭圆型问题的数值解

4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2023-01-01 DOI: 10.1553/etna_vol59s179

Zorica Milovanović Jeknić, Bratislav Sredojević, Dejan Bojović

引用次数: 0

Optimal averaged Padé-type approximants 最优平均padvac -type近似

4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2023-01-01 DOI: 10.1553/etna_vol59s145

Dusan Lj. Djukić, Rada M. Mutavdžić Djukić, Lothar Reichel, Miodrag M. Spalević

引用次数: 1

Inexact rational Krylov subspace methods for approximating the action of functions of matrices 逼近矩阵函数作用的非精确有理Krylov子空间方法

4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2023-01-01 DOI: 10.1553/etna_vol58s538

Shengjie Xu, Fei Xue

{"title":"Inexact rational Krylov subspace methods for approximating the action of functions of matrices","authors":"Shengjie Xu, Fei Xue","doi":"10.1553/etna_vol58s538","DOIUrl":"https://doi.org/10.1553/etna_vol58s538","url":null,"abstract":"This paper concerns the theory and development of inexact rational Krylovsubspace methods for approximating the action of a function of a matrix $f(A)$to a column vector $b$. At each step of the rational Krylov subspace methods, ashifted linear system of equations needs to be solved to enlarge the subspace.For large-scale problems, such a linear system is usually solved approximatelyby an iterative method. The main question is how to relax the accuracy of theselinear solves without negatively affecting the convergence of the approximationof $f(A)b$. Our insight into this issue is obtained by exploring the residualbounds for the rational Krylov subspace approximations of $f(A)b$, based on thedecaying behavior of the entries in the first column of certain matrices of $A$restricted to the rational Krylov subspaces. The decay bounds for these entriesfor both analytic functions and Markov functions can be efficiently andaccurately evaluated by appropriate quadrature rules. A heuristic based on thesebounds is proposed to relax the tolerances of the linear solves arising in eachstep of the rational Krylov subspace methods. As the algorithm progresses towardconvergence, the linear solves can be performed with increasingly lower accuracyand computational cost. Numerical experiments for large nonsymmetric matricesshow the effectiveness of the tolerance relaxation strategy for the inexactlinear solves of rational Krylov subspace methods.","PeriodicalId":50536,"journal":{"name":"Electronic Transactions on Numerical Analysis","volume":"61 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Symmetrization techniques in image deblurring 图像去模糊中的对称技术

4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2023-01-01 DOI: 10.1553/etna_vol59s157

Marco Donatelli, Paola Ferrari, Silvia Gazzola

引用次数: 0

Gauss-type quadrature rules with respect to external zeros of the integrand 关于被积函数外零的高斯型正交规则

4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2023-01-01 DOI: 10.1553/etna_vol59s230

Jelena Tomanović

{"title":"Gauss-type quadrature rules with respect to external zeros of the integrand","authors":"Jelena Tomanović","doi":"10.1553/etna_vol59s230","DOIUrl":"https://doi.org/10.1553/etna_vol59s230","url":null,"abstract":"In the present paper, we propose a Gauss-type quadrature rule into which the external zeros of the integrand (the zeros of the integrand outside the integration interval) are incorporated. This new formula with $n$ nodes, denoted by $mathcal G_n$, proves to be exact for certain polynomials of degree greater than $2n-1$ (while the Gauss quadrature formula with the same number of nodes is exact for all polynomials of degree less than or equal to $2n-1$). It turns out that $mathcal G_n$ has several good properties: all its nodes are pairwise distinct and belong to the interior of the integration interval, all its weights are positive, it converges, and it is applicable both when the external zeros of the integrand are known exactly and when they are known approximately. In order to economically estimate the error of $mathcal G_n$, we construct its extensions that inherit the $n$ nodes of $mathcal G_n$ and that are analogous to the Gauss-Kronrod, averaged Gauss, and generalized averaged Gauss quadrature rules. Further, we show that $mathcal G_n$ with respect to the pairwise distinct external zeros of the integrand represents a special case of the (slightly modified) Gauss quadrature formula with preassigned nodes. The accuracy of $mathcal G_n$ and its extensions is confirmed by numerical experiments.","PeriodicalId":50536,"journal":{"name":"Electronic Transactions on Numerical Analysis","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135261952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Perturbation analysis of matrices over a quaternion division algebra 四元数除法代数上矩阵的微扰分析

IF 1.3 4区数学

Electronic Transactions on Numerical Analysis Pub Date : 2021-01-01 DOI: 10.1553/ETNA_VOL54S128

Sk. Safique Ahmad, I. Ali, I. Slapničar

引用次数: 1