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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
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
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
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
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
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
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
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)
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
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
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
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
Compositio Mathematica Comptes Rendus Mathématique Computing Constructive Approximation COSMOS Crelle's Journal (Journal fuer die Reine und Angewandte
List_of_mathematics_journals
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
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
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
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
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
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)
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
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
Branch of mathematics
studies functions, spaces, and operators through quantitative methods of approximation and convergence. It grew out of calculus, especially the use of derivatives
Mathematical_analysis
Russian-American mathematician
Ronald DeVore, Constructive approximation, Springer Verlag 1993 with Manfred von Golitschek, and Yuli Makovoz: Constructive approximation: advanced problems
George_G._Lorentz
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
"Sparse components of images and optimal atomic decompositions." Constructive Approximation 17.3 (2001): 353–382. "PDF". CiteSeerX 10.1.1.379.8993. Guo, Kanghui
Shearlet
American mathematician
Complex Variables and Elliptic Equations International Journal, the Constructive Approximation mathematical journal, the American Mathematical Monthly, the Journal
Lee_Albert_Rubel
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
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
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
the Whitney inequality gives an upper bound for the error of best approximation of a function by polynomials in terms of the moduli of smoothness. It
Whitney_inequality
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
Models". Constructive Approximation. 55 (1): 369–406. doi:10.1007/s00365-021-09549-y. ISSN 1432-0940. Barron, A.R. (May 1993). "Universal approximation bounds
Barron_space
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
\mathbb {N} .} DeVore, Ronald A.; Lorentz, George G. (1993). Constructive approximation. Grundlehren der mathematischen Wissenschaften. Vol. 303. Springer
Modulus_of_smoothness
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
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
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
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
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
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
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
Lebesgue constants DeVore, Ronald A.; Lorentz, George G. (1993). Constructive approximation. Grundlehren der mathematischen Wissenschaften. Vol. 303. Berlin:
Lebesgue's_lemma
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Type of neural network which utilizes recursion
backpropagation through time used for recurrent neural networks. The universal approximation capability of RNNs over trees has been proved in literature. Recurrent
Recursive_neural_network
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
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
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
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)
On bipartite matching and vertex cover
largest size of a matching equals the smallest size of a vertex cover. The constructive proof described above provides an algorithm for producing a minimum vertex
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
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
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
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
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
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
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
Distance over which a wave's shape repeats
their spacing. In the figure I1 has been set to unity, a very rough approximation. The effect of interference is to redistribute the light, so the energy
Wavelength
Large number used in number theory
non-trivial zeros of the Riemann zeta function. The largest error term in the approximation π ( x ) ≈ li ( x ) {\displaystyle \pi (x)\approx \operatorname {li}
Skewes's_number
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
Theorem in topology
non-constructive indirect proofs, they ran contrary to Brouwer's intuitionist ideals. Although the existence of a fixed point is not constructive in the
Brouwer_fixed-point_theorem
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
On constructing objects that obey a system of constraints with limited dependence
"A constructive proof of the Lovász Local Lemma". arXiv:0810.4812 [cs.DS].. Piotr Berman, Marek Karpinski and Alexander D. Scott, Approximation Hardness
Algorithmic Lovász local lemma
Algorithmic_Lovász_local_lemma
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
Continuous function on an interval takes on every value between its values at the ends
(2020-04-15). "Intermediate value theorem for simplices for simplicial approximation of fixed points and zeros". Topology and Its Applications. 275 107036
Intermediate_value_theorem
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
Binary sequence
any G δ {\displaystyle G_{\delta }} set determined by a constructive null cover. Constructive martingales (Schnorr 1971): A martingale is a function d
Algorithmically random sequence
Algorithmically_random_sequence
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
Optical interference pattern of concentric rings
lens, R, the air gap between the glass surfaces, t, is given to a good approximation by t = r 2 2 R , {\displaystyle t={r^{2} \over 2R},} where the effect
Newton's_rings
Set of principles for modeling solid geometry
especially when used in conjunction with other representations such as constructive solid geometry. This scheme follows from the combinatoric (algebraic
Solid_modeling
Recreational mathematics planar boundary and area problem
of tan − 1 {\displaystyle \tan ^{-1}} , or an approximation method like Newton–Raphson. A constructive way to obtain a quick and very accurate estimate
Goat_grazing_problem
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
Signal processing technique for sensor arrays
antenna array in such a way that signals at particular angles experience constructive interference while others experience destructive interference. Beamforming
Beamforming
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
Region of space between a transmitting and receiving antenna
the phase difference between the two waves, the waves can interfere constructively or destructively. In any wave-propagated transmission between a transmitter
Fresnel_zone
Type of algebraic integer
rediscovered by G. H. Hardy in 1919 within the context of Diophantine approximation. They became widely known after the publication of Charles Pisot's dissertation
Pisot–Vijayaraghavan_number
Surface in 3D space defined by an implicit function of three variables
P. Gomes (2019). "Pi-surfaces: products of implicit surfaces towards constructive composition of 3D objects". WSCG 2019 27. International Conference in
Implicit_surface
Element mapped to itself by a mathematical function
761–783. doi:10.1137/0211062. Patrick Cousot; Radhia Cousot (1979). "Constructive Versions of Tarski's Fixed Point Theorems" (PDF). Pacific Journal of
Fixed_point_(mathematics)
Type of artificial neural network architecture
Nakamura et al. (1993) created activation functions with guaranteed approximation accuracy. These works linked KART's theoretical potential with practical
Kolmogorov–Arnold_Networks
Boolean function
Pitassi, Toniann (2006). "Monotone Circuits for the Majority Function". Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Majority_function
Force resisting sliding motion
2018-04-20. De Saxcé, G.; Feng, Z.-Q. (1998). "The bipotential method: A constructive approach to design the complete contact law with friction and improved
Friction
Intelligence of 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
CONSTRUCTIVE APPROXIMATION
CONSTRUCTIVE APPROXIMATION
Girl/Female
Tamil
Creation, Construction, Arrangement
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Creation; Evolution; Construction
Girl/Female
Hindu
Creation, Construction, Arrangement
Girl/Female
Tamil
Creation, Construction, Arrangement
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
Girl/Female
Indian
Built; Construction; Creative Art; All Creation
Girl/Female
Tamil
Light, Beauty, Prosperity, Rank, Power, Steel construction company
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
Hindu, Indian, Marathi
Produce; New Construction
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
CONSTRUCTIVE APPROXIMATION
CONSTRUCTIVE APPROXIMATION
Girl/Female
Hebrew
Grace or bitter.
Male
Egyptian
, a mystical serpent.
Boy/Male
Scandinavian French
a shelter.
Girl/Female
Tamil
Illuminated
Female
Chinese
flowery tuber.
Boy/Male
Hindu, Indian
Wanderer Traveller
Boy/Male
English
Little rock.
Boy/Male
Hindu
Lord Vishnu
Surname or Lastname
English
English : variant of Province.
Boy/Male
English French
Derived from a surname introduced into Britain during the Norman Conquest, based on the the...
CONSTRUCTIVE APPROXIMATION
CONSTRUCTIVE APPROXIMATION
CONSTRUCTIVE APPROXIMATION
CONSTRUCTIVE APPROXIMATION
CONSTRUCTIVE APPROXIMATION
a.
Building up; constructive; -- opposed to destructive.
adv.
In a constructive manner; by construction or inference.
n.
The act of fabricating, framing, or constructing; construction; manufacture; as, the fabrication of a bridge, a church, or a government.
a.
Constructive.
a.
Building; constructing.
n.
The act of constructing; construction.
n.
An obstructive person or thing.
n.
That which is constructed or formed; an edifice; a fabric.
a.
Derived from, or depending on, construction or interpretation; not directly expressed, but inferred.
a.
According to interpretation; constructive.
a.
Reconstructing; tending to reconstruct; as, a reconstructive policy.
a.
Conveying knowledge; serving to instruct or inform; as, experience furnishes very instructive lessons.
a.
Pertaining to a master builder, or to architecture; evincing skill in designing or construction; constructive.
a.
Serving or tending to bind or constrict.
a.
Obstructive.
n.
The act of constructing vaults; a vaulted construction.
n.
The process or art of constructing; the act of building; erection; the act of devising and forming; fabrication; composition.
n.
The method of construing, interpreting, or explaining a declaration or fact; an attributed sense or meaning; understanding; explanation; interpretation; sense.
a.
Having ability to construct or form; employed in construction; as, to exhibit constructive power.
n.
Instructive discourse.