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Academic journal
Constructive Approximation is "an international mathematics journal dedicated to Approximations, expansions, and related research in: computation, function
Constructive_Approximation
Property of artificial neural networks
Yarotsky, Dmitry (2021). "Universal Approximations of Invariant Maps by Neural Networks". Constructive Approximation. 55: 407–474. arXiv:1804.10306. doi:10
Universal approximation theorem
Universal_approximation_theorem
Theory of getting acceptably close inexact mathematical calculations
Journal of Approximation Theory Constructive Approximation East Journal on Approximations Estimation theory Fourier series Function approximation Numerical
Approximation_theory
Mathematical function
or time-limited. They are widely used as basis functions for constructive approximation and in linear inverse problems, and as apodization tapers or window
Slepian_function
Class of algorithms that find approximate solutions to optimization problems
shortest such tour. A classic example of approximation algorithm providing an additive guarantee is the constructive proof of Vizing’s theorem. It shows how
Approximation_algorithm
Inverse of the gamma function
Henrik (9 September 2013). ""Inverses of gamma functions"". Constructive Approximation. 7 (2): 251–267. arXiv:1309.2167. doi:10.1007/s00365-014-9239-1
Inverse_gamma_function
Field of mathematical analysis
analysis, constructive function theory is a field which studies the connection between the smoothness of a function and its degree of approximation. It is
Constructive_function_theory
Italian mathematician and professor
Dolomites Research Notes on Approximation published by the Padua University Press, coordinator of the Constructive Approximation and Applications Research
Stefano_De_Marchi
Method in machine learning
"Learning Theory Estimates via Integral Operators and Their Approximations". Constructive Approximation. 26 (2): 153–172. CiteSeerX 10.1.1.210.722. doi:10
Early_stopping
Russian-American mathematician
Ronald DeVore, Constructive approximation, Springer Verlag 1993 with Manfred von Golitschek, and Yuli Makovoz: Constructive approximation: advanced problems
George_G._Lorentz
Analytic function with prescribed zeros
Powers of a Blaschke Factor and Strongly Annular Functions". Constructive Approximation. 60 (1): 33–86. doi:10.1007/s00365-023-09650-4. Borichev, Alexander;
Blaschke_product
Generalization of Sobolev spaces
Russian). 126: 1163–1165. MR 0107165. DeVore, R. and Lorentz, G. "Constructive Approximation", 1993. DeVore, R., Kyriazis, G. and Wang, P. "Multiscale characterizations
Besov_space
Mathematical theorem in the study of analysis
outlines a constructive proof of the above theorem. For differentiable functions, Jackson's inequality bounds the error of approximations by polynomials
Stone–Weierstrass_theorem
the de Bruijn-Newman constant Λ, and the Riemann hypothesis". Constructive Approximation. 10 (1): 107–129. doi:10.1007/BF01205170. MR 1260363. S2CID 122664556
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
representation and projection theorem Journals: Constructive Approximation Journal of Approximation Theory Extrapolation Linear predictive analysis —
List of numerical analysis topics
List_of_numerical_analysis_topics
Theorem in complex analysis
Mergelyan's theorem is a result from approximation by polynomials in complex analysis proved by the Armenian mathematician Sergei Mergelyan in 1951. Let
Mergelyan's_theorem
American mathematician
for Constructive Approximation and was from 2004 to 2007 the Executive Dean of the College of Arts and Sciences. His research deals with approximation of
Edward_B._Saff
Soviet mathematician
Akademie Verlag. 1955. Natanson, I. P. (1964). Constructive function theory. Vol. I. Uniform approximation. Translated by Alexis N. Obolensky. New York:
Isidor_Natanson
Compositio Mathematica Comptes Rendus Mathématique Computing Constructive Approximation COSMOS Crelle's Journal (Journal fuer die Reine und Angewandte
List_of_mathematics_journals
Mathematical result
proof of the restricted isometry property for random matrices", Constructive Approximation, 28 (3): 253–263, doi:10.1007/s00365-007-9003-x, hdl:1911/21683
Johnson–Lindenstrauss_lemma
Belgian mathematician
Dolomites Workshop on Constructive Approximation and Applications, in 2016, and a special issue of the Dolomites Research Notes on Approximation, published in
Annie_Cuyt
Multivariate functions can be written using univariate functions and summing
Griebel, Michael (2009). "On a constructive proof of Kolmogorov's superposition theorem". Constructive Approximation. 30 (3): 653–675. doi:10.1007/s00365-009-9054-2
Kolmogorov–Arnold representation theorem
Kolmogorov–Arnold_representation_theorem
Egyptian mathematician
the editorial boards of several journals including Constructive Approximation, Journal of Approximation Theory, Journal of Physics A, and The Ramanujan Journal
Mourad_Ismail
Pair of zeros of the Riemann zeta function
the de Bruijn-Newman constant Λ, and the Riemann hypothesis", Constructive Approximation, 10 (1): 107–129, doi:10.1007/BF01205170, MR 1260363, S2CID 122664556
Lehmer_pair
Branch of mathematics
mathematics that studies functions, spaces, and operators through methods of approximation and convergence. It grew out of calculus, especially the use of derivatives
Mathematical_analysis
Series of advanced mathematics textbooks
George G. Lorentz: Constructive Approximation. 1993 George G. Lorentz, Manfred von Golitschek, Yuly Makovoz: Constructive Approximation: Advanced Problems
Grundlehren der mathematischen Wissenschaften
Grundlehren_der_mathematischen_Wissenschaften
"Sparse components of images and optimal atomic decompositions." Constructive Approximation 17.3 (2001): 353–382. "PDF". CiteSeerX 10.1.1.379.8993. {{cite
Shearlet
NP-hard problem in combinatorial optimization
optimal. It was one of the first approximation algorithms, and was in part responsible for drawing attention to approximation algorithms as a practical approach
Travelling_salesman_problem
Q-analog of the ordinary derivative
(2018) Basics of Post-Quantum Calculus. In: Recent Advances in Constructive Approximation Theory. SpringerOptimization and Its Applications, vol 138. Springer
Q-derivative
Soviet mathematician
foundations of constructive function theory, a field studying the connection between smoothness properties of a function and its approximations by polynomials
Sergei_Bernstein
Unique positive real number which when multiplied by itself gives 2
fraction 99/70 (≈ 1.4142857) is sometimes used as a good rational approximation with a reasonably small denominator. Sequence A002193 in the On-Line
Square_root_of_2
Process in machine learning and statistics
Yarotsky, Dmitry (2021-04-30). "Universal Approximations of Invariant Maps by Neural Networks". Constructive Approximation. 55: 407–474. arXiv:1804.10306. doi:10
Feature_selection
In approximation theory, a converse to Jackson's theorem
continuous. Bernstein's lethargy theorem Constructive function theory Achieser, N.I. (1956). Theory of Approximation. New York: Frederick Ungar Publishing
Bernstein's theorem (approximation theory)
Bernstein's_theorem_(approximation_theory)
(1998). "Uniform asymptotic expansion for Meixner polynomials". Constructive Approximation. 14 (1): 113–150. doi:10.1007/s003659900066. Jin, X.-S.; Wong
Meixner_polynomials
American mathematician (1928–1983)
on analysis. He is best known for developing constructive analysis in his 1967 Foundations of Constructive Analysis, where he proved most of the important
Errett_Bishop
Philosphical view that existence proofs must be constructive
proof by contradiction might be called non-constructive, and a constructivist might reject it. The constructive viewpoint involves a verificational interpretation
Constructivism (philosophy of mathematics)
Constructivism_(philosophy_of_mathematics)
Lebesgue constants DeVore, Ronald A.; Lorentz, George G. (1993). Constructive Approximation. A Series of Comprehensive Studies in Mathematics. Vol. 303. Berlin
Lebesgue's_lemma
Mathematical analysis
In mathematics, constructive analysis is mathematical analysis done according to some principles of constructive mathematics. The name of the subject contrasts
Constructive_analysis
American mathematician
matrices and conditionally positive definite functions" (PDF). Constructive Approximation. 2 (1): 11–22. doi:10.1007/BF01893414. (over 2160 citations) Micchelli
Charles_Anthony_Micchelli
Type of polynomial used in Numerical Analysis
Polynomials in this form were first used by Bernstein in a constructive proof of the Weierstrass approximation theorem. With the advent of computer graphics, Bernstein
Bernstein_polynomial
Interference phenomenon of waves
for diffraction based on the concepts proposed by Fresnel as well as approximations needed to apply them. In general, all these approaches require formulating
Diffraction
Elliptic analog of hypergeometric series
transformation formulas for elliptic hypergeometric series", Constructive Approximation, 18 (4): 479–502, arXiv:math/0001006, doi:10.1007/s00365-002-0501-6
Elliptic hypergeometric series
Elliptic_hypergeometric_series
Family of basic hypergeometric orthogonal polynomials in the basic Askey scheme
difference operators and symmetric Al-Salam–Chihara polynomials. Constructive Approximation, 28(2), 199-218. Ishikawa, M., & Zeng, J. (2009). The Andrews–Stanley
Al-Salam–Chihara_polynomials
American mathematician
Complex Variables and Elliptic Equations International Journal, the Constructive Approximation mathematical journal, the American Mathematical Monthly, the Journal
Lee_Albert_Rubel
partition has been proved before, but Simmons' proof also yields a constructive approximation algorithm. For example, assume that a certain land-estate has
Simmons–Su_protocols
Polynomial whose coefficients are all 1 or −1
(2016). "The Mahler measure of the Rudin–Shapiro polynomials". Constructive Approximation. 43 (3): 357–369. doi:10.1007/s00365-015-9297-z. Erdélyi, Tamás
Littlewood_polynomial
Asymptotic analysis used when integrating rapidly-varying complex exponentials
In mathematics, the stationary phase approximation is a basic principle of asymptotic analysis, applying to functions given by integration against a rapidly-varying
Stationary phase approximation
Stationary_phase_approximation
the Flow-Induced Function Spaces for Neural Network Models". Constructive Approximation. 55 (1): 369–406. arXiv:1906.08039. doi:10.1007/s00365-021-09549-y
Barron_space
Identity for a sequence of orthogonal polynomials
Christoffel–Darboux Kernel Via Three-Term Recurrence Relation I". Constructive Approximation. 54 (1): 49–116. arXiv:1909.09107. doi:10.1007/s00365-020-09519-w
Christoffel–Darboux_formula
\mathbb {N} .} DeVore, Ronald A.; Lorentz, George G. (1993). Constructive approximation. Grundlehren der mathematischen Wissenschaften. Vol. 303. Springer
Modulus_of_smoothness
Israeli mathematician
(1992). "Polynomial approximation in L p {\displaystyle L_{p}} ( 0 < p < 1 {\displaystyle 0<p<1} )". Constructive Approximation. 8 (2): 187–201. doi:10
Dany_Leviatan
Mathematics concept
polynomials and properties of Student-t distributions" (PDF). Constructive Approximation. 27: 15–32. doi:10.1007/s00365-006-0643-6. Retrieved 2006-08-16
Bessel_polynomials
Theorem about metric spaces
a constructive method to find those fixed points. It can be understood as an abstract formulation of Picard's method of successive approximations. The
Banach_fixed-point_theorem
Mathematical inequality
ISSN 1443-5756. Zbl 1060.30003. Natanson, I.P. (1964). Constructive function theory. Volume I: Uniform approximation. Translated by Alexis N. Obolensky. New York:
Bernstein's theorem (polynomials)
Bernstein's_theorem_(polynomials)
Topics referred to by the same term
complex numbers Constructive function theory, the study of the connection between the smoothness of a function and its degree of approximation Geometric function
Function_theory
Interpolation Spaces §4 Two Theorems of Whitney: Theorem 4.2". Constructive Approximation. Grundlehren der mathematischen Wissenschaften. Vol. 303. Springer
Whitney_inequality
On bipartite matching and vertex cover
from the point of view of exact solutions, they are not equivalent for approximation algorithms. Bipartite maximum matchings can be approximated arbitrarily
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Function returning one of only two values
The set of Walsh transforms of the components is known as a linear approximation table (LAT) or correlation matrix; it describes the correlation between
Boolean_function
Armenian mathematician
mathematician, who made major contributions to the Approximation theory. The modern Complex Approximation Theory is based on Mergelyan's classical work. Corresponding
Sergey_Mergelyan
Wave phenomenon
proportion of the wavelength. Numerical approximations may be used, including the Fresnel and Fraunhofer approximations. Because diffraction is the result
Diffraction_from_slits
Decomposition of periodic functions
sums (Fourier series) of lengths 1, 2, 3, and 4 terms, showing how the approximation to a square wave improves as the number of terms increases (animation)
Fourier_series
Real number that can be computed within arbitrary precision
representing computable reals, and Cantor's diagonal argument cannot be used constructively to demonstrate uncountably many of them. While the set of real numbers
Computable_number
Method of drawing geometric objects
must have a finite number of steps and not be the limit of ever-closer approximations. Stated this way, straightedge-and-compass constructions appear to be
Straightedge and compass construction
Straightedge_and_compass_construction
Type of neural network which utilizes recursion
of 3D shape structures in the form of cuboid abstractions. RecCC is a constructive neural network approach to deal with tree domains with pioneering applications
Recursive_neural_network
Soviet mathematician
Ukraine) was a Soviet mathematician. He is known for his work in the constructive function theory, in particular, for the Remez algorithm and the Remez
Evgeny_Yakovlevich_Remez
after James H. Bramble and Stephen Hilbert, bounds the error of an approximation of a function u {\displaystyle \textstyle u} by a polynomial of order
Bramble–Hilbert_lemma
Continuous function on an interval takes on every value between its values at the ends
dimension, gives a special case of the intermediate value theorem. In constructive mathematics, the intermediate value theorem is not true. Instead, the
Intermediate_value_theorem
Type of artificial neural network
neural networks for classification, regression, clustering, sparse approximation, compression and feature learning with a single layer or multiple layers
Extreme_learning_machine
Force resisting sliding motion
than providing an estimate of the actual frictional force, the Coulomb approximation provides a threshold value for this force, above which motion would
Friction
Number that is not a ratio of integers
A Constructive Approach through Interval Arithmetic. John Wiley & Sons. ISBN 978-1-470-45144-8. Errett Bishop; Douglas Bridges (1985). Constructive Analysis
Irrational_number
Russian mathematician (1856–1922)
(1903–1979), was also a notable mathematician, making contributions to constructive mathematics and recursive function theory. Andrey Markov was born on
Andrey_Markov
Optical illusion
k = 0.75 {\displaystyle k=0.75} (green) in Fig. 3 corresponds to an approximation in which the objective half-angle A {\displaystyle A} was assumed to
Globe_effect
differs from classical analysis. Constructive function theory a branch of analysis that is closely related to approximation theory, studying the connection
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Soviet mathematician
3 June 1980) was a Soviet and Ukrainian mathematician known for his works in approximation theory and the theory of differential and integral operators. He is
Naum_Akhiezer
Fundamental principle of physics
generally only approximately linear, the superposition principle is only an approximation of the true physical behavior. The superposition principle applies to
Superposition_principle
Optical interference pattern of concentric rings
lens, R, the air gap between the glass surfaces, t, is given to a good approximation by t=r22R, where the effect of viewing the pattern at an angle oblique
Newton's_rings
original (PDF) on 2015-09-19. Lloyd N. Trefethen (2013). Approximation Theory and Approximation Practice. SIAM. p. 211. ISBN 978-1-611972-39-9. Agronomof
List of mathematical constants
List_of_mathematical_constants
Topological space with a dense countable subset
numerical analysis and constructive mathematics, since many theorems that can be proved for nonseparable spaces have constructive proofs only for separable
Separable_space
Computer science award
Madhu; Szegedy, Mario (1998), "Proof verification and the hardness of approximation problems" (PDF), Journal of the ACM, 45 (3): 501–555, CiteSeerX 10.1
Gödel_Prize
Branch of mathematics
object. Reformulations of calculus in a constructive framework are generally part of the subject of constructive analysis. While many of the ideas of calculus
Calculus
Inequality on approximations of a function by algebraic or trigonometric polynomials
Bernstein's theorem. See also constructive function theory. Achiezer (Akhiezer), N.I. (2013) [1956]. Theory of approximation. Translated by Hyman, C.J. Dover
Jackson's_inequality
Chemical theory
conclusions of the Woodward–Hoffmann rules. Fukui realized that a good approximation for reactivity could be found by looking at the frontier orbitals (HOMO/LUMO)
Frontier molecular orbital theory
Frontier_molecular_orbital_theory
Riemannian manifold with SU(n) holonomy
combined symmetry constraints, neural metric approximations and symbolic regression to derive compact approximations to Ricci-flat metrics. Lee and Lukas independently
Calabi–Yau_manifold
Function in mathematical analysis
Constructive analysis Modulus of convergence Lévy's modulus of continuity theorem for Brownian motion Legendre transform and Lipschitz approximation Choquet
Modulus_of_continuity
Concept in genetics
1\end{cases}}} where γ {\displaystyle \gamma } is Euler's constant. The first approximation represents the waiting time until the first mutant destined for loss
Genetic_drift
Taiwanese-born New Zealand mathematician
sciences with honours in 1998, and a PhD in 2001. Her dissertation, Constructive approaches to quasi-Monte Carlo methods for multiple integration, was
Frances_Kuo
Unsolved problem in computer science
Gasarch, W. "Computational complexity". Aviad Rubinstein's Hardness of Approximation Between P and NP, winner of the ACM's 2017 Doctoral Dissertation Award
P_versus_NP_problem
Distance over which a wave's shape repeats
principle. When sinusoidal waveforms add, they may reinforce each other (constructive interference) or cancel each other (destructive interference) depending
Wavelength
Swedish mathematician and concert pianist
had been open for more than forty years: The basis problem and the approximation problem and later the invariant subspace problem for Banach spaces.
Per_Enflo
Condition for a mathematical function to map some value to itself
point. By contrast, the Brouwer fixed-point theorem (1911) is a non-constructive result: it says that any continuous function from the closed unit ball
Fixed-point_theorem
Predecessor to modern quantum mechanics (1900–1925)
mechanics. The theory has come to be understood as the semi-classical approximation to modern quantum mechanics. The main and final accomplishments of the
Old_quantum_theory
Representation of a graph as a path graph "thickened" by some amount
The best known approximation ratio of a polynomial time approximation algorithm for pathwidth is O((log n)3/2). For earlier approximation algorithms for
Pathwidth
Multipath radio propagation model
height, two waves are added constructively to yield bigger power. As distance increases, these waves add up constructively and destructively, giving regions
Two-ray ground-reflection model
Two-ray_ground-reflection_model
Fair item allocation problem
non-constructive. Asadpour, Feige and Saberi proved that the integrality gap of the configuration linear program is 1/4. The implies a 1/4-approximation algorithm
Egalitarian_item_allocation
In mathematics, invariant of square matrices
ISBN 978-0-321-28713-7 Lombardi, Henri; Quitté, Claude (2015), Commutative Algebra: Constructive Methods, Springer, ISBN 9789401799447 Mac Lane, Saunders (1998), Categories
Determinant
Type of algorithm, produces approximately correct solutions
whose solution is also a solution to the initial problem. An example of approximation is described by Jon Bentley for solving the travelling salesman problem
Heuristic_(computer_science)
Problem in computer science
[Hilbert] was only angry and frustrated, but then he began to try to deal constructively with the problem... Gödel himself felt—and expressed the thought in
Halting_problem
Study of algorithms in strategic environments
notion of approximation ratio in algorithm design. The existence of an equilibrium in a game is typically established using non-constructive fixed point
Algorithmic_game_theory
Intelligence in machines
some of Dreyfus's comments. Had he formulated them less aggressively, constructive actions they suggested might have been taken much earlier." Searle presented
Artificial_intelligence
Physical model of propagating energy
example, in optics two or more coherent light waves may interact and by constructive or destructive interference yield a resultant irradiance deviating from
Electromagnetic_radiation
travel, tourism, insurance
CONSTRUCTIVE APPROXIMATION
CONSTRUCTIVE APPROXIMATION
Girl/Female
Hindu
Creation, Construction, Arrangement
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sanskrit, Sindhi, Tamil, Telugu
Construction; Arrangement; Creative Art; All Creation
Surname or Lastname
English
English : local name for someone who lived in a small cottage or temporary dwelling, Middle English logge (Old French loge, of Germanic origin). The term was used in particular of a cabin erected by masons working on the site of a particular construction project, such as a church or cathedral, and so it was probably in many cases equivalent to an occupational name for a mason. Reaney suggests that one early form, atte Logge, might sometimes have denoted the warden of a masons’ lodge.Henry Cabot Lodge (1850–1924), the influential U.S. senator from MA, was born in Boston, the only son of John Ellerton Lodge, a prosperous merchant and owner of swift clipper ships engaged in commerce with China, one of several Lodges who emigrated from England in the 18th and 19th centuries.
Girl/Female
Indian
Built; Construction; Creative Art; All Creation
Girl/Female
Tamil
Creation, Construction, Arrangement
Boy/Male
Arabic, Muslim
A Persian Construction Probably from the Arabic Mawla (Master; Leader; Lord)
Girl/Female
Hindu
Light, Beauty, Prosperity, Rank, Power, Steel construction company
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Creation; Evolution; Construction
Girl/Female
Tamil
Creation, Construction, Arrangement
Girl/Female
Hindu, Indian, Marathi
Produce; New Construction
Girl/Female
Hindu
Creation, Construction, Arrangement
Girl/Female
Tamil
Light, Beauty, Prosperity, Rank, Power, Steel construction company
CONSTRUCTIVE APPROXIMATION
CONSTRUCTIVE APPROXIMATION
CONSTRUCTIVE APPROXIMATION
CONSTRUCTIVE APPROXIMATION
CONSTRUCTIVE APPROXIMATION
CONSTRUCTIVE APPROXIMATION
CONSTRUCTIVE APPROXIMATION
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