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Constant upper bounds on the matrix exponential norm 矩阵指数范数的常数上界
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-02-01 DOI: 10.1515/rnam-2022-0002
Y. Nechepurenko, G. Zasko
{"title":"Constant upper bounds on the matrix exponential norm","authors":"Y. Nechepurenko, G. Zasko","doi":"10.1515/rnam-2022-0002","DOIUrl":"https://doi.org/10.1515/rnam-2022-0002","url":null,"abstract":"Abstract This work is devoted to the constant (time-independent) upper bounds on the function ∥ exp(tA)∥2 where t ⩾ 0 and A is a square matrix whose eigenvalues have negative real parts. Along with some constant upper bounds obtained from known time-dependent exponential upper bounds based on the solutions of Lyapunov equations, a new constant upper bound is proposed that has significant advantages. A detailed comparison of all these constant upper bounds is carried out using 2 × 2 matrices and matrices of medium size from the well-known NEP collection.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47556151","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
Frontmatter
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-02-01 DOI: 10.1515/rnam-2022-frontmatter1
{"title":"Frontmatter","authors":"","doi":"10.1515/rnam-2022-frontmatter1","DOIUrl":"https://doi.org/10.1515/rnam-2022-frontmatter1","url":null,"abstract":"Article Frontmatter was published on February 1, 2022 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 37, issue 1).","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495406","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
On numerical computation of sensitivity of response functions to system inputs in variational data assimilation problems 变分同化问题中响应函数对系统输入灵敏度的数值计算
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-02-01 DOI: 10.1515/rnam-2022-0004
V. Shutyaev, T. T. Hà, F. Le Dimet, H. S. Hoang, N. H. Phong
{"title":"On numerical computation of sensitivity of response functions to system inputs in variational data assimilation problems","authors":"V. Shutyaev, T. T. Hà, F. Le Dimet, H. S. Hoang, N. H. Phong","doi":"10.1515/rnam-2022-0004","DOIUrl":"https://doi.org/10.1515/rnam-2022-0004","url":null,"abstract":"Abstract Prediction of pollution in water flow is a very important task. To this end, it is imperative to be able to define the uncertainty in a model prediction. This is the purpose of sensitivity analysis whose role is to identify what uncertainty in the model outputs is attributable to the model inputs (parameters in this case). Traditionally, this is achieved by running the model perturbed by many random samples in the parameter space to determine their impact on the model outputs. It provides information on how much of the output variance is controlled by each parameter of the inputs. The theoretical results related to the procedure based adjoint approach for computing a sensitivity of the response function (RF) to changes in the input source are presented in the paper. It is shown that this approach allows to compute, by one single integration of the adjoint equation over a given time interval, a sensitivity of the RF to any source located in the domain of interest. The proposed approach is applied to the 2D Saint-Venant flow equations for modelling the water pollution problem. A numerical experiment is formulated and implemented for the Thanh Nhan Lake in Hanoi for studying a sensitivity of some RF to observations. The numerical model is constructed by applying the well-known finite-volume method. Two appropriate optimization problems are introduced and solved on the basis of the BFGS algorithm. The numerical results show the efficiency of the proposed method and confirm the theoretical findings.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48246963","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: 2
Sketching for a low-rank nonnegative matrix approximation: Numerical study 低秩非负矩阵近似的速写:数值研究
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-01-26 DOI: 10.1515/rnam-2023-0009
S. Matveev, S. Budzinskiy
{"title":"Sketching for a low-rank nonnegative matrix approximation: Numerical study","authors":"S. Matveev, S. Budzinskiy","doi":"10.1515/rnam-2023-0009","DOIUrl":"https://doi.org/10.1515/rnam-2023-0009","url":null,"abstract":"Abstract We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose factors can be arbitrary. We calculate the computational complexities of the proposed methods and evaluate their performance in numerical experiments. The comparison with the known deterministic alternating projection methods shows that the randomized approaches are faster and exhibit similar convergence properties.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42931067","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: 3
Frontmatter
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-12-01 DOI: 10.1515/rnam-2021-frontmatter6
{"title":"Frontmatter","authors":"","doi":"10.1515/rnam-2021-frontmatter6","DOIUrl":"https://doi.org/10.1515/rnam-2021-frontmatter6","url":null,"abstract":"","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43713542","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
Numerical-statistical study of the prognostic efficiency of the SEIR model SEIR模型预测效率的数值统计研究
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-12-01 DOI: 10.1515/rnam-2021-0027
G. Lotova, V. Lukinov, M. Marchenko, G. Mikhailov, D. Smirnov
{"title":"Numerical-statistical study of the prognostic efficiency of the SEIR model","authors":"G. Lotova, V. Lukinov, M. Marchenko, G. Mikhailov, D. Smirnov","doi":"10.1515/rnam-2021-0027","DOIUrl":"https://doi.org/10.1515/rnam-2021-0027","url":null,"abstract":"Abstract A comparative analysis of the differential and the corresponding stochastic Poisson SEIR-models is performed for the test problem of COVID-19 epidemic in Novosibirsk modelling the period from March 23, 2020 to June 21, 2020 with the initial population N = 2 798 170. Varying the initial population in the form N = n m with m ⩾ 2, we show that the average numbers of identified sick patients is less (beginning from April 7, 2020) than the corresponding differential values by the quantity that does not differ statistically from C(t)/m, with C ≈ 27.3 on June 21, 2020. This relationship allows us to use the stochastic model for big population N. The practically useful ‘two sigma’ confidential interval for the time interval from June 1, 2020 to June 21, 2020 is about 108% (as to the statistical average) and involves the corresponding real statistical estimates. The influence of the introduction of delay on the prognosis, i.e., the incubation period corresponding to Poisson model is also studied.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43771417","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
General finite-volume framework for saddle-point problems of various physics 各种物理鞍点问题的一般有限体积框架
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-12-01 DOI: 10.1515/rnam-2021-0029
K. Terekhov
{"title":"General finite-volume framework for saddle-point problems of various physics","authors":"K. Terekhov","doi":"10.1515/rnam-2021-0029","DOIUrl":"https://doi.org/10.1515/rnam-2021-0029","url":null,"abstract":"Abstract This article is dedicated to the general finite-volume framework used to discretize and solve saddle-point problems of various physics. The framework applies the Ostrogradsky–Gauss theorem to transform a divergent part of the partial differential equation into a surface integral, approximated by the summation of vector fluxes over interfaces. The interface vector fluxes are reconstructed using the harmonic averaging point concept resulting in the unique vector flux even in a heterogeneous anisotropic medium. The vector flux is modified with the consideration of eigenvalues in matrix coefficients at vector unknowns to address both the hyperbolic and saddle-point problems, causing nonphysical oscillations and an inf-sup stability issue. We apply the framework to several problems of various physics, namely incompressible elasticity problem, incompressible Navier–Stokes, Brinkman–Hazen–Dupuit–Darcy, Biot, and Maxwell equations and explain several nuances of the application. Finally, we test the framework on simple analytical solutions.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47028589","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: 2
An equilibrated a posteriori error estimator for an Interior Penalty Discontinuous Galerkin approximation of the p-Laplace problem p-拉普拉斯问题的内罚不连续伽辽金近似的平衡后验误差估计
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-12-01 DOI: 10.1515/rnam-2021-0026
R. Hoppe, Youri Iliash
{"title":"An equilibrated a posteriori error estimator for an Interior Penalty Discontinuous Galerkin approximation of the p-Laplace problem","authors":"R. Hoppe, Youri Iliash","doi":"10.1515/rnam-2021-0026","DOIUrl":"https://doi.org/10.1515/rnam-2021-0026","url":null,"abstract":"Abstract We are concerned with an Interior Penalty Discontinuous Galerkin (IPDG) approximation of the p-Laplace equation and an equilibrated a posteriori error estimator. The IPDG method can be derived from a discretization of the associated minimization problem involving appropriately defined reconstruction operators. The equilibrated a posteriori error estimator provides an upper bound for the discretization error in the broken W1,p norm and relies on the construction of an equilibrated flux in terms of a numerical flux function associated with the mixed formulation of the IPDG approximation. The relationship with a residual-type a posteriori error estimator is established as well. Numerical results illustrate the performance of both estimators.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41567420","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
Stability analysis of functionals in variational data assimilation with respect to uncertainties of input data for a sea thermodynamics model 关于海洋热力学模型输入数据不确定性的变分数据同化中泛函的稳定性分析
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-12-01 DOI: 10.1515/rnam-2021-0028
V. Shutyaev, E. Parmuzin, I. Gejadze
{"title":"Stability analysis of functionals in variational data assimilation with respect to uncertainties of input data for a sea thermodynamics model","authors":"V. Shutyaev, E. Parmuzin, I. Gejadze","doi":"10.1515/rnam-2021-0028","DOIUrl":"https://doi.org/10.1515/rnam-2021-0028","url":null,"abstract":"Abstract The problem of stability and sensitivity of functionals of the optimal solution of the variational data assimilation of sea surface temperature for the model of sea thermodynamics is considered. The variational data assimilation problem is formulated as an optimal control problem to find the initial state and the boundary heat flux. The sensitivity of the response functions as functionals of the optimal solution with respect to the observation data is studied. Computing the gradient of the response function reduces to the solution of a non-standard problem being a coupled system of direct and adjoint equations with mutually dependent initial and boundary values. The algorithm to compute the gradient of the response function is presented, based on the Hessian of the original cost functional. Stability analysis of the response function with respect to uncertainties of input data is given. Numerical examples are presented for the Black and Azov seas thermodynamics model.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41918039","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: 2
Frontmatter Frontmatter
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-11-01 DOI: 10.1515/rnam-2021-frontmatter5
{"title":"Frontmatter","authors":"","doi":"10.1515/rnam-2021-frontmatter5","DOIUrl":"https://doi.org/10.1515/rnam-2021-frontmatter5","url":null,"abstract":"","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46386755","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
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