Constructive Approximation最新文献

Extremal Polynomials and Sets of Minimal Capacity 极值多项式和最小容量集

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-09-11 DOI: 10.1007/s00365-024-09690-4

Jacob S. Christiansen, Benjamin Eichinger, Olof Rubin

引用次数: 0

Uniform Approximation of Continuous Couplings 连续耦合的均匀逼近

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-07-16 DOI: 10.1007/s00365-023-09660-2

Ugo Bindini, Tapio Rajala

引用次数: 0

On the Characteristic Polynomial of the Eigenvalue Moduli of Random Normal Matrices 论随机正态矩阵特征值模的特征多项式

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-05-25 DOI: 10.1007/s00365-024-09689-x

Sung-Soo Byun, Christophe Charlier

引用次数: 0

Constructing Embedded Lattice-Based Algorithms for Multivariate Function Approximation with a Composite Number of Points 构建基于嵌入式网格的多变量函数逼近复合点算法

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-04-29 DOI: 10.1007/s00365-024-09688-y

Frances Y. Kuo, Weiwen Mo, Dirk Nuyens

{"title":"Constructing Embedded Lattice-Based Algorithms for Multivariate Function Approximation with a Composite Number of Points","authors":"Frances Y. Kuo, Weiwen Mo, Dirk Nuyens","doi":"10.1007/s00365-024-09688-y","DOIUrl":"https://doi.org/10.1007/s00365-024-09688-y","url":null,"abstract":"We approximate d-variate periodic functions in weighted Korobov spaces with general weight parameters using n function values at lattice points. We do not limit n to be a prime number, as in currently available literature, but allow any number of points, including powers of 2, thus providing the fundamental theory for construction of embedded lattice sequences. Our results are constructive in that we provide a component-by-component algorithm which constructs a suitable generating vector for a given number of points or even a range of numbers of points. It does so without needing to construct the index set on which the functions will be represented. The resulting generating vector can then be used to approximate functions in the underlying weighted Korobov space. We analyse the approximation error in the worst-case setting under both the (L_2) and (L_{infty }) norms. Our component-by-component construction under the (L_2) norm achieves the best possible rate of convergence for lattice-based algorithms, and the theory can be applied to lattice-based kernel methods and splines. Depending on the value of the smoothness parameter (alpha ), we propose two variants of the search criterion in the construction under the (L_{infty }) norm, extending previous results which hold only for product-type weight parameters and prime n. We also provide a theoretical upper bound showing that embedded lattice sequences are essentially as good as lattice rules with a fixed value of n. Under some standard assumptions on the weight parameters, the worst-case error bound is independent of d.","PeriodicalId":50621,"journal":{"name":"Constructive Approximation","volume":"11 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 a Class of Elliptic Orthogonal Polynomials and their Integrability 论一类椭圆正交多项式及其可积分性

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-04-19 DOI: 10.1007/s00365-024-09687-z

Harini Desiraju, Tomas Lasic Latimer, Pieter Roffelsen

引用次数: 0

Expected Energy of Zeros of Elliptic Polynomials 椭圆多项式零点的期望能量

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-04-12 DOI: 10.1007/s00365-024-09684-2

Víctor de la Torre, Jordi Marzo

引用次数: 0

Approximation and Interpolation of Singular Measures by Trigonometric Polynomials 用三角多项式对奇异量进行逼近和插值

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-04-04 DOI: 10.1007/s00365-024-09686-0

Paul Catala, Mathias Hockmann, Stefan Kunis, Markus Wageringel

引用次数: 0

Ferrers Functions of Arbitrary Degree and Order and Related Functions 任意度和阶的费勒斯函数及相关函数

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-04-02 DOI: 10.1007/s00365-024-09683-3

引用次数: 0

Matrix Continued Fractions Associated with Lattice Paths, Resolvents of Difference Operators, and Random Polynomials 与晶格路径、差分算子的残差和随机多项式相关的矩阵续分数

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-03-22 DOI: 10.1007/s00365-024-09685-1

J. Kim, A. López-García, V. A. Prokhorov

{"title":"Matrix Continued Fractions Associated with Lattice Paths, Resolvents of Difference Operators, and Random Polynomials","authors":"J. Kim, A. López-García, V. A. Prokhorov","doi":"10.1007/s00365-024-09685-1","DOIUrl":"https://doi.org/10.1007/s00365-024-09685-1","url":null,"abstract":"We begin our analysis with the study of two collections of lattice paths in the plane, denoted ({mathcal {D}}_{[n,i,j]}) and ({mathcal {P}}_{[n,i,j]}). These paths consist of sequences of n steps, where each step allows movement in three directions: upward (with a maximum displacement of q units), rightward (exactly one unit), or downward (with a maximum displacement of p units). The paths start from the point (0, i) and end at the point (n, j). In the collection ({mathcal {D}}_{[n,i,j]}), it is a crucial constraint that paths never go below the x-axis, while in the collection ({mathcal {P}}_{[n,i,j]}), paths have no such restriction. We assign weights to each path in both collections and introduce weight polynomials and generating series for them. Our main results demonstrate that certain matrices of size (qtimes p) associated with these generating series can be expressed as matrix continued fractions. These results extend the notable contributions previously made by Flajolet (Discrete Math 32:125–161, 1980) and Viennot (Une Théorie Combinatoire des Polynômes Orthogonaux Généraux. University of Quebec at Montreal, Lecture Notes, 1983) in the scalar case (p=q=1). The generating series can also be interpreted as resolvents of one-sided or two-sided difference operators of finite order. Additionally, we analyze a class of random banded matrices H, which have (p+q+1) diagonals with entries that are independent and bounded random variables. These random variables have identical distributions along diagonals. We investigate the asymptotic behavior of the expected values of eigenvalue moments for the principal (ntimes n) truncation of H as n tends to infinity.","PeriodicalId":50621,"journal":{"name":"Constructive Approximation","volume":"1 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Metric Approximation of Set-Valued Functions of Bounded Variation by Integral Operators 用积分算子对有界变化的集值函数进行度量逼近

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-03-13 DOI: 10.1007/s00365-024-09681-5

Elena E. Berdysheva, Nira Dyn, Elza Farkhi, Alona Mokhov

{"title":"Metric Approximation of Set-Valued Functions of Bounded Variation by Integral Operators","authors":"Elena E. Berdysheva, Nira Dyn, Elza Farkhi, Alona Mokhov","doi":"10.1007/s00365-024-09681-5","DOIUrl":"https://doi.org/10.1007/s00365-024-09681-5","url":null,"abstract":"We introduce an adaptation of integral approximation operators to set-valued functions (SVFs, multifunctions), mapping a compact interval [a, b] into the space of compact non-empty subsets of ({mathbb {R}}^d). All operators are adapted by replacing the Riemann integral for real-valued functions by the weighted metric integral for SVFs of bounded variation with compact graphs. For such a SVF F, we obtain pointwise error estimates for sequences of integral operators at points of continuity, leading to convergence at such points to F. At points of discontinuity of F, we derive estimates, which yield the convergence to a certain set described in terms of the metric selections of F. To obtain these estimates we refine and extend known results on approximation of real-valued functions by integral operators. Our analysis uses recently defined one-sided local quasi-moduli at points of discontinuity and several notions of local Lipschitz property at points of continuity. We also provide a global approach for error bounds. A multifunction F is represented by the set of all its metric selections, while its approximation (its image under the operator) is represented by the set of images of these metric selections under the operator. A bound on the Hausdorff distance between these two sets of single-valued functions in (L^1) provides our global estimates. The theory is applied to concrete operators: the Bernstein–Durrmeyer operator and the Kantorovich operator.\u0000","PeriodicalId":50621,"journal":{"name":"Constructive Approximation","volume":"3 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140127045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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