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kolmogorov n-width (26) 26
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ADVANCES IN COMPUTATIONAL MATHEMATICS, ISSN 1019-7168, 12/2019, Volume 45, Issue 5-6, pp. 2273 - 2286
Kolmogorov n-widths and Hankel singular values are two commonly used concepts in model reduction. Here, we show that for the special case of linear... 
MATHEMATICS, APPLIED | REDUCED-BASIS APPROXIMATIONS | RATES | PARTIAL-DIFFERENTIAL-EQUATIONS | NONLINEAR-SYSTEMS | Kolmogorov n-width | Active subspaces | Model reduction | Hankel operator | Reduced basis method | MODEL ORDER REDUCTION | PRIORI CONVERGENCE THEORY | Hankel singular values
Journal Article
数学学报:英文版, ISSN 1439-8516, 2015, Volume 31, Issue 9, pp. 1475 - 1486
Journal Article
Set-Valued and Variational Analysis, ISSN 1877-0533, 3/2016, Volume 24, Issue 1, pp. 83 - 99
The problem of computing the asymptotic order of the Kolmogorov n-width of the unit ball of the space of multivariate periodic functions induced by a... 
Geometry | Kolmogorov n -widths | Non-degenerate differential operator | 41A63 | Analysis | Convex duality | 41A10 | Mathematics | Asymptotic order | 41A50 | Kolmogorov n-widths | MATHEMATICS, APPLIED | SPACES | HYPERBOLIC CROSSES | MIXED SMOOTHNESS
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2006, Volume 75, Issue 253, pp. 241 - 258
Let S_{\beta}:=\{z\in {\mathbb C}:|{\rm Im}z|<\beta\} be a strip in complex plane. \widetilde{H}_{\infty,\beta}^{r} denotes those 2\pi-periodic, real-valued... 
Integers | Zero | Mathematical theorems | Approximation | Analytic functions | Rolles theorem | Information economics | Mathematical functions | Polynomials | Kolmogorov type comparison theorem | n-widths | Hardy-Sobolev class | N-widths | Hardy–Sobolev class | MATHEMATICS, APPLIED | PERIODIC-FUNCTIONS | OPTIMAL RECOVERY | OPERATORS | ANALYTIC-FUNCTIONS
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 2009, Volume 157, Issue 1, pp. 19 - 31
We consider relative widths characterizing the best approximation of a fixed set by its sections of given dimension. For Sobolev classes W p 1 on [ 0 , 1 ]... 
Relative [formula omitted]-width of a function class | Approximation of Sobolev classes | Kolmogorov width | Width of a function class | Relative n-width of a function class | MATHEMATICS
Journal Article
Mathematical Notes, ISSN 0001-4346, 6/2011, Volume 89, Issue 5, pp. 645 - 651
We describe isometric embeddings of the Wiener spiral in complex Hilbert space and obtain the asymptotics of the Kolmogorov n-widths of specific embeddings. We... 
complex Hilbert space | real Hilbert space | isometric embedding | Kolmogorov n-width | Mathematics, general | Mathematics | Wiener spiral | correlation function of a mapping | Hermitian kernel | MATHEMATICS
Journal Article
Analysis in Theory and Applications, ISSN 1672-4070, 6/2007, Volume 23, Issue 2, pp. 180 - 187
In this paper, we give some optimal algorithms for diagonal operator T from space l p (1 ≦ p ≦ 2) to l 2 on n-widths in different computational setting. 
41A46 | linear average n-width | Analysis | Kolmogorov n-width | 47A58 | Approximations and Expansions | linear stochastic n-width | Mathematics | linear n-width | 42A61 | Linear n-width | Linear stochastic n-width | Linear average n-width
Journal Article
by Lang, J
Journal of Approximation Theory, ISSN 0021-9045, 2006, Volume 140, Issue 2, pp. 141 - 146
Consider the Hardy-type operator T : L p ( a , b ) → L p ( a , b ) ,- ∞ ⩽ a < b ⩽ ∞ , which is defined by ( Tf ) ( x ) = v ( x ) ∫ a x u ( t ) f ( t ) dt . It... 
Weighted Hardy-type operators | Kolmogorov | Integral operators | Approximation | Weighted spaces | Gel’fand and Bernstein numbers | Gel'fand and Bernstein numbers | MATHEMATICS | weighted spaces | approximation | weighted hardy-type operators | integral operators | Geffand and Bernstein numbers
Journal Article
Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 10/2017, Volume 57, Issue 10, pp. 1559 - 1576
Journal Article
Annals of Functional Analysis, ISSN 2008-8752, 2015, Volume 6, Issue 4, pp. 114 - 133
Weakly singular Volterra integral equations of the different types are considered. The construction of accuracy-optimal numerical methods for one-dimensional... 
Optimal approximation | Volterra integral equation | Collocation method | Babenko and kolmogorov n-widths | Weakly singular kernel | collocation method | MATHEMATICS | MATHEMATICS, APPLIED | weakly singular kernel | Babenko and Kolmogorov n-widths | optimal approximation
Journal Article
Mathematical Notes, ISSN 0001-4346, 3/2002, Volume 71, Issue 3, pp. 477 - 485
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 05/1993, Volume 39, Issue 3, pp. 930 - 945
Journal Article
Complex Analysis and Operator Theory, ISSN 1661-8254, 05/2009, Volume 3, Issue 2, pp. 501 - 524
Let $$G \subset{\mathbb{C}}$$ be a bounded simply connected domain with boundary Γ and let $$E \subset G$$ be a regular compact set with connected complement.... 
Operator Theory | 30E10 | Analysis | extremal problems | Mathematics, general | Kolmogorov n -width | Mathematics | potential theory | 41A16 | Potential theory | Extremal problems | Kolmogorov n-width | MATHEMATICS | MATHEMATICS, APPLIED | ANALYTIC-FUNCTIONS | Universities and colleges
Journal Article
Siberian Mathematical Journal, ISSN 0037-4466, 5/2005, Volume 46, Issue 3, pp. 535 - 539
We find an estimate for the nth minimal error of linear algorithms for some problem defined in a finite-dimensional space with values in an arbitrary normed... 
Mathematics, general | Kolmogorov n -width | Mathematics | minimal error of linear algorithms | least norm polynomial | Minimal error of linear algorithms | Kolmogorov n-width | Least norm polynomial | MATHEMATICS
Journal Article
Constructive Approximation, ISSN 0176-4276, 1/2008, Volume 27, Issue 1, pp. 99 - 120
Presenting a unified approach, we establish a Kolmogorov-type comparison theorem for classes of 2π-periodic functions defined by a special class of operators... 
Numerical Analysis | Analysis | Mathematics | Comparison theorems of Kolmogorov type | Oscillation properties | n-widths | MATHEMATICS | PERIODIC-FUNCTIONS | APPROXIMATION | oscillation properties | n-Widths | VALUES | ANALYTIC-FUNCTIONS | comparison theorems of Kolmogorov type
Journal Article
Mathematical Notes, ISSN 0001-4346, 7/2006, Volume 80, Issue 1, pp. 11 - 18
The sharp Jackson-type inequalities obtained by Taikov in the space L 2 and containing the best approximation and the modulus of continuity of first order are... 
Gelfand n-widths | width of function classes | Kolmogorov | Mathematics, general | Mathematics | Bernstein | periodic function | Jackson-type inequalities | modulus of continuity of kth order | Modulus of continuity of kth order | Periodic function | Width of function classes | MATHEMATICS
Journal Article
Mathematical Notes, ISSN 0001-4346, 11/2002, Volume 72, Issue 5, pp. 615 - 619
Journal Article
by CHEN, H
CHINESE ANNALS OF MATHEMATICS SERIES B, ISSN 0252-9599, 07/1991, Volume 12, Issue 3, pp. 272 - 281
Let B approximately p(r),1 = {f: g(r-1) is abs. cont. on I = [a, b], f is periodic with periodic with period H(= b - a), f(x1) = 0, parallel-to f(r)... 
MATHEMATICS
Journal Article
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