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Keywords
(1)
Moving Least Square
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Moving leastsquares are BackusGilbert optimal
Moving leastsquares are BackusGilbert optimal,10.1016/00219045(89)900907,Journal of Approximation Theory,L. Bos,K. Salkauskas
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Moving leastsquares are BackusGilbert optimal
(
Citations: 18
)
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L. Bos
,
K. Salkauskas
Journal:
Journal of Approximation Theory  JAT
, vol. 59, no. 3, pp. 267275, 1989
DOI:
10.1016/00219045(89)900907
Cumulative
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linkinghub.elsevier.com
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Citation Context
(7)
...The preferred construction for MLS shape functions, the socalled Backus–Gilbert approach [
4
], seeks a quasiinterpolant of the form (7) such that:...
Robert Brownlee
,
et al.
Enhancing SPH using Moving LeastSquares and Radial Basis Functions
...The relationship between MLS and G.Backus and F. Gilbert [2] theory was found by Abramovici [1] for Shepard’s method and for the general case by Bos and Salkauskas [
3
]...
Soonjeong Ahn
,
et al.
3D Surface Reconstruction from Scattered Data Using Moving Least Squar...
...Beside the application oriented investigation of Shepard’s method such as [4] (see also [3,14,20,23,22,
5
]), an increasing interest has arisen from mathematical researchers to examine the approximation property of formula (10)...
Domonkos Tikk
,
et al.
Stability of interpolative fuzzy KH controllers
...However, it brings us back to the BackusGilbert theory [BG1][BG3], [
BS
]...
...The connection between the moving leastsquares method and the BackusGilbert theory is shown by Abramovici [Ab] for Shepard’s method, and for the general case by Bos and Salkauskas [
BS
]...
...The BackusGilbert approach [BG1][BG3] is exactly in the form of the constrained leastsquares problem (2.1)(2.2), with only J = 1 in (2.2) and p1 1. The general case is discussed in [
BS
]...
...Part 3 of Proposition 1 reasserts the connection between the moving leastsquares method and the BackusGilbert optimality which was shown by Abramovici [Ab] for Shepard’s method, and for the more general case by Bos and Salkauskas [
BS
]...
David Levin
.
The approximation power of moving leastsquares
...The Shepard operator (1.1) is an interpolatory operator widely used in approximation theory and in fitting data, curves, and surfaces (see, e.g., [1], [
3
][9], [11], [12], [14] [18] and the references given therein)...
B. Della Vecchia
.
Direct and converse results by rational operators
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Citations
(18)
Stable Moving LeastSquares
Yaron Lipman
Journal:
Journal of Approximation Theory  JAT
, vol. 161, no. 1, pp. 371384, 2009
Gradient incorporation in onedimensional applications of interpolating moving leastsquares methods for fitting potential energy surfaces
(
Citations: 2
)
Igor V. Tokmakov
,
Albert F. Wagner
,
Michael Minkoff
,
Donald L. Thompson
Journal:
Theoretical Chemistry Accounts  THEOR CHEM ACC
, vol. 118, no. 4, pp. 755767, 2007
Enhancing SPH using Moving LeastSquares and Radial Basis Functions
(
Citations: 1
)
Robert Brownlee
,
Paul Houston
,
Jeremy Levesley
,
Stephan Rosswog
Published in 2007.
Hermite type movingleastsquares approximations
(
Citations: 1
)
Z. Komargodski
,
D. Levin
Journal:
Computers & Mathematics With Applications  COMPUT MATH APPL
, vol. 51, no. 8, pp. 12231232, 2006
Dual bases and discrete reproducing kernels: a unified framework for RBF and MLS approximation
(
Citations: 3
)
G. E. Fasshauer
Journal:
Engineering Analysis With Boundary Elements  ENG ANAL BOUND ELEM
, vol. 29, no. 4, pp. 313325, 2005