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Moving least-squares are Backus-Gilbert optimal

Moving least-squares are Backus-Gilbert optimal,10.1016/0021-9045(89)90090-7,Journal of Approximation Theory,L. Bos,K. Salkauskas

Moving least-squares are Backus-Gilbert optimal   (Citations: 18)
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Journal: Journal of Approximation Theory - JAT , vol. 59, no. 3, pp. 267-275, 1989
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    • ...The preferred construction for MLS shape functions, the so-called Backus–Gilbert approach [4], seeks a quasi-interpolant of the form (7) such that:...

    Robert Brownleeet al. Enhancing SPH using Moving Least-Squares 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]...

    Soon-jeong Ahnet 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 Tikket al. Stability of interpolative fuzzy KH controllers

    • ...However, it brings us back to the Backus-Gilbert theory [BG1]-[BG3], [BS]...
    • ...The connection between the moving least-squares method and the Backus-Gilbert theory is shown by Abramovici [Ab] for Shepard’s method, and for the general case by Bos and Salkauskas [BS]...
    • ...The Backus-Gilbert approach [BG1]-[BG3] is exactly in the form of the constrained least-squares 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 least-squares method and the Backus-Gilbert 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 least-squares

    • ...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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