# Difference operators from interpolating moving least squares and their deviation from optimality

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 39, Issue: 5, page 883-908
- ISSN: 0764-583X

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topSonar, Thomas. "Difference operators from interpolating moving least squares and their deviation from optimality." ESAIM: Mathematical Modelling and Numerical Analysis 39.5 (2010): 883-908. <http://eudml.org/doc/194292>.

@article{Sonar2010,

abstract = {
We consider the classical Interpolating Moving Least Squares (IMLS)
interpolant as defined by Lancaster and Šalkauskas [Math. Comp.37 (1981)
141–158] and
compute the first and second derivative of this interpolant at the nodes of a
given grid with the help of a basic lemma on Shepard interpolants. We compare
the difference formulae with those defining optimal finite difference methods and
discuss their deviation from optimality.
},

author = {Sonar, Thomas},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Difference operators; moving least squares interpolation; order of approximation.; order of approximation; Shepard interpolant},

language = {eng},

month = {3},

number = {5},

pages = {883-908},

publisher = {EDP Sciences},

title = {Difference operators from interpolating moving least squares and their deviation from optimality},

url = {http://eudml.org/doc/194292},

volume = {39},

year = {2010},

}

TY - JOUR

AU - Sonar, Thomas

TI - Difference operators from interpolating moving least squares and their deviation from optimality

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 39

IS - 5

SP - 883

EP - 908

AB -
We consider the classical Interpolating Moving Least Squares (IMLS)
interpolant as defined by Lancaster and Šalkauskas [Math. Comp.37 (1981)
141–158] and
compute the first and second derivative of this interpolant at the nodes of a
given grid with the help of a basic lemma on Shepard interpolants. We compare
the difference formulae with those defining optimal finite difference methods and
discuss their deviation from optimality.

LA - eng

KW - Difference operators; moving least squares interpolation; order of approximation.; order of approximation; Shepard interpolant

UR - http://eudml.org/doc/194292

ER -

## References

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