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Application of Ensemble Kalman Smoothing in Inverse Modeling of Advection and Diffusion 卡尔曼平滑法在平流和扩散逆建模中的应用
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-09-13 DOI: 10.1134/s1995423924030030
E. G. Klimova
{"title":"Application of Ensemble Kalman Smoothing in Inverse Modeling of Advection and Diffusion","authors":"E. G. Klimova","doi":"10.1134/s1995423924030030","DOIUrl":"https://doi.org/10.1134/s1995423924030030","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>To study the spread of greenhouse gases in space and time, as well as to assess the fluxes of these gases from the Earth’s surface by using a data assimilation system is an important problem of monitoring the environment. One of the approaches to estimating the greenhouse gas fluxes is based on the assumption that the fluxes are constant in a given subdomain and over a given time interval (about a week). This is justified by the properties of the algorithm and the observational data used. The modern problems of estimating greenhouse gas fluxes from the Earth’s surface have large dimensions. Therefore, a problem statement is usually considered in which the fluxes are estimated, and an advection and diffusion model is included in the observation operator. Here we deal with large assimilation windows in which fluxes are estimated in several time intervals. The paper considers an algorithm for estimating the fluxes based on observations from a given time interval. The algorithm is a variant of an ensemble smoothing algorithm, which is widely used in such problems. It is shown that when using an assimilation window in which the fluxes are estimated for several time intervals, the algorithm may become unstable, and an observability condition is violated.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"55 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258765","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
How a Unitoid Matrix Loses Its Unitoidness? 类空矩阵如何失去类空性？
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-09-13 DOI: 10.1134/s1995423924030029
Kh. D. Ikramov, A. M. Nazari
{"title":"How a Unitoid Matrix Loses Its Unitoidness?","authors":"Kh. D. Ikramov, A. M. Nazari","doi":"10.1134/s1995423924030029","DOIUrl":"https://doi.org/10.1134/s1995423924030029","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A unitoid is a square matrix that can be brought to diagonal form by a congruence transformation. Among different diagonal forms of a unitoid <span>(A)</span>, there is only one, up to the order adopted for the principal diagonal, whose nonzero diagonal entries all have the modulus 1. It is called the congruence canonical form of <span>(A)</span>, while the arguments of the nonzero diagonal entries are called the canonical angles of <span>(A)</span>. If <span>(A)</span> is nonsingular then its canonical angles are closely related to the arguments of the eigenvalues of the matrix <span>(A^{-*}A)</span>, called the cosquare of <span>(A)</span>. Although the definition of a unitoid reminds the notion of a diagonalizable matrix in the similarity theory, the analogy between these two matrix classes is misleading. We show that the Jordan block <span>(J_{n}(1))</span>, which is regarded as an antipode of diagonalizability in the similarity theory, is a unitoid. Moreover, its cosquare <span>(C_{n}(1))</span> has <span>(n)</span> distinct unimodular eigenvalues. Then we immerse <span>(J_{n}(1))</span> in the family of the Jordan blocks <span>(J_{n}(lambda))</span>, where <span>(lambda)</span> is varying in the range <span>((0,2])</span>. At some point to the left of 1, <span>(J_{n}(lambda))</span> is not a unitoid any longer. We discuss this moment in detail in order to comprehend how it can happen. Similar moments with even smaller <span>(lambda)</span> are discussed, and certain remarkable facts about the eigenvalues of cosquares and their condition numbers are pointed out.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"11 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258768","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
Criteria of Solvability for Asymmetric Difference Schemes at High-Accuracy Approximation of Boundary Conditions 高精度近似边界条件下非对称差分方案的可解性标准
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-09-13 DOI: 10.1134/s1995423924030066
V. I. Paasonen
{"title":"Criteria of Solvability for Asymmetric Difference Schemes at High-Accuracy Approximation of Boundary Conditions","authors":"V. I. Paasonen","doi":"10.1134/s1995423924030066","DOIUrl":"https://doi.org/10.1134/s1995423924030066","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper we study a technology of calculating difference problems with internal boundary conditions of flux balance constructed by means of one-sided multipoint difference analogs of first derivatives of arbitrary order of accuracy. The technology is suitable for any type of differential equations to be solved and admits the same type of realization at any order of accuracy. In contrast to the approximations based on an extended system of equations, this technology does not lead to complications in splitting multidimensional problems into one-dimensional ones. Sufficient conditions of solvability and stability are formulated for realizations of the algorithms by using the double-sweep method for boundary conditions of arbitrary order of accuracy. Their proof is based on a reduction of the multipoint boundary conditions to a form that does not violate the tridiagonal structure of the matrices and the establishment of conditions of diagonal dominance in the transformed matrix rows corresponding to the external and internal boundary conditions.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"39 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258770","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
On Existence and Numerical Solution of a New Class of Nonlinear Second Degree Integro-Differential Volterra Equation with Convolution Kernel 带卷积核的新一类非线性二阶积分微分 Volterra 方程的存在性与数值解法
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-09-13 DOI: 10.1134/s1995423924030042
S. Lemita, M L. Guessoumi
{"title":"On Existence and Numerical Solution of a New Class of Nonlinear Second Degree Integro-Differential Volterra Equation with Convolution Kernel","authors":"S. Lemita, M L. Guessoumi","doi":"10.1134/s1995423924030042","DOIUrl":"https://doi.org/10.1134/s1995423924030042","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper considers a new class of nonlinear second degree integro-differential Volterra equation with a convolution kernel. We derive some sufficient conditions to establish the existence and uniqueness of solutions by using Schauder fixed point theorem. Moreover, the Nyström method is applied to obtain the approximate solution of the proposed Volterra equation. A numerical examples are given to validate the adduced results.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"17 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258766","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
An Explicit Finite Difference Approximation for Space-Time Riesz–Caputo Variable Order Fractional Wave Equation Using Hermitian Interpolation 利用赫米特插值法实现时空里兹-卡普托变阶分数波方程的显式有限差分近似法
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-09-13 DOI: 10.1134/s1995423924030054
Chol Won O, Won Myong Ro, Yun Chol Kim
{"title":"An Explicit Finite Difference Approximation for Space-Time Riesz–Caputo Variable Order Fractional Wave Equation Using Hermitian Interpolation","authors":"Chol Won O, Won Myong Ro, Yun Chol Kim","doi":"10.1134/s1995423924030054","DOIUrl":"https://doi.org/10.1134/s1995423924030054","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Variable order fractional operators can be used in various physical and biological applications where rates of change of the quantity of interest may depend on space and/or time. In this paper, we propose an explicit finite difference approximation for space-time Riesz–Caputo variable order fractional wave equation with initial and boundary conditions in a finite domain. The proposed scheme is conditionally stable and has global truncation error <span>(O(tau^{2}+h^{2}))</span>. We also present a numerical experiment to verify the efficiency of the proposed scheme.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"206 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258769","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
Numerical Solution of the One-Dimensional Forward Magnetotelluric Sounding Problem Using a Computational Grid Adaptation Approach 使用计算网格适应方法数值求解一维前向磁层探测问题
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-09-13 DOI: 10.1134/s1995423924030078
S. N. Sklyar, O. B. Zabinyakova
{"title":"Numerical Solution of the One-Dimensional Forward Magnetotelluric Sounding Problem Using a Computational Grid Adaptation Approach","authors":"S. N. Sklyar, O. B. Zabinyakova","doi":"10.1134/s1995423924030078","DOIUrl":"https://doi.org/10.1134/s1995423924030078","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper considers an implementation of an adaptive computational grid constructing algorithm in a numerical solution of the one-dimensional forward magnetotelluric sounding problem (the Tikhonov–Cagniard problem). The numerical solution of the problem is realized by a method of local integral equations which was proposed by the authors previously. The adaptive computational grid construction is based on geometrical principles of optimizing a piecewise constant interpolant of the electrical conductivity function to be approximated. Numerical experiments are carried out to study and illustrate the effectiveness of the combined method. The algorithm is tested on the Kato–Kikuchi model with a known exact solution.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"29 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258771","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
Partial Multivariate Errors-in-Variables Model and Its Application in Settlement Monitoring 部分多变量变量误差模型及其在结算监测中的应用
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-09-13 DOI: 10.1134/s1995423924030017
Q. Wang, F. Hu
{"title":"Partial Multivariate Errors-in-Variables Model and Its Application in Settlement Monitoring","authors":"Q. Wang, F. Hu","doi":"10.1134/s1995423924030017","DOIUrl":"https://doi.org/10.1134/s1995423924030017","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Aiming at the problem that the coefficient matrix of multivariate errors-in-variables (MEIV) model contains constant columns, the MEIV model is extended to Partial multivariate errors-in-variables (P-MEIV), and the new algorithm of P-MEIV model is proposed based on the principle of Partial errors-in-variables (PEIV) model and indirect adjustment. The algorithm is simple and easy to implement. An example of coordinate transformation is used for verifying, and the results are compared with the existing MEIV model algorithm, which shows the effectiveness of the proposed algorithm. Finally, the P-MEIV algorithm is applied to the multi-point grey model (MGM(1,N)) of settlement monitoring. The results show that the P-MEIV model proposed in this paper can better consider the influence of monitoring point errors, and the estimated results are in good agreement with the actual situation.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"42 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258767","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
An Approximate Algorithm for Simulating Stationary Discrete Random Processes with Bivariate Distributions of Their Consecutive Components in the Form of Mixtures of Gaussian Distributions 模拟具有高斯分布混合物形式连续成分双变量分布的静态离散随机过程的近似算法
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-05-28 DOI: 10.1134/s199542392402006x
V. A. Ogorodnikov, M. S. Akenteva, N. A. Kargapolova
{"title":"An Approximate Algorithm for Simulating Stationary Discrete Random Processes with Bivariate Distributions of Their Consecutive Components in the Form of Mixtures of Gaussian Distributions","authors":"V. A. Ogorodnikov, M. S. Akenteva, N. A. Kargapolova","doi":"10.1134/s199542392402006x","DOIUrl":"https://doi.org/10.1134/s199542392402006x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper presents an approximate algorithm for modeling a stationary discrete random process with marginal and bivariate distributions of its consecutive components in the form of a mixture of two Gaussian distributions. The algorithm is based on a combination of the conditional distribution method and the rejection method. An example of application of the proposed algorithm for simulating time series of daily maximum air temperatures is given.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"49 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171487","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
Choice of Approximation Bases Used in Computational Functional Algorithms for Approximating Probability Densities on the Basis of Given Sample 基于给定样本的概率密度近似计算函数算法中所用近似基础的选择
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-05-28 DOI: 10.1134/s1995423924020022
A. V. Voytishek, N. Kh. Shlimbetov
{"title":"Choice of Approximation Bases Used in Computational Functional Algorithms for Approximating Probability Densities on the Basis of Given Sample","authors":"A. V. Voytishek, N. Kh. Shlimbetov","doi":"10.1134/s1995423924020022","DOIUrl":"https://doi.org/10.1134/s1995423924020022","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper we formulate requirements for choosing approximation bases when constructing cost-effective optimized computational (numerical) functional algorithms for approximating probability densities on the basis of a given sample, with special attention paid to the stability and approximation of the bases. It is shown that to meet the requirements and construct efficient approaches to conditional optimization of numerical schemes, the best choice is a multi-linear approximation and the corresponding special case for both kernel and projection computational algorithms for nonparametric density estimation, which is a multidimensional analogue of the frequency polygon.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"65 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171564","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
Numerical Stochastic Simulation of Spatially Heterogeneous Population 空间异质性种群的数值随机模拟
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-05-28 DOI: 10.1134/s1995423924020071
N. V. Pertsev, V. A. Topchii, K. K. Loginov
{"title":"Numerical Stochastic Simulation of Spatially Heterogeneous Population","authors":"N. V. Pertsev, V. A. Topchii, K. K. Loginov","doi":"10.1134/s1995423924020071","DOIUrl":"https://doi.org/10.1134/s1995423924020071","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A continuous-discrete stochastic model is constructed to describe the evolution of a spatially heterogeneous population. The population structure is defined in terms of a graph with two vertices and two unidirectional edges. The graph describes the presence of individuals in the population at the vertices and their transitions between the vertices along the edges. Individuals enter the population to each of the vertices of the graph from an external source. The duration of the migration of individuals along the edges of the graph is constant. Individuals may die or turn into individuals of other populations not considered in the model. The assumptions of the model are formulated, and a probabilistic formalization of the model and a numerical simulation algorithm based on the Monte Carlo method are given. The laws of population size distribution are studied. The results of a computational experiment are presented.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"40 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171641","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
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