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Interpolating moving least-squares methods for fitting potential energy surfaces: Improving efficiency via local approximants
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10.1063/1.2805084
/content/aip/journal/jcp/127/21/10.1063/1.2805084
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/21/10.1063/1.2805084

Figures

Image of FIG. 1.
FIG. 1.

The rms error for energy as a function of for second degree IMLS (panel a) and third degree IMLS (panel b) using 501 (circles) and 2001 (triangles) symmetry distinct points. is defined as the distance to the nearest point. The filled symbols are for and the open ones for .

Image of FIG. 2.
FIG. 2.

The rms error vs for the second degree IMLS (filled circles) and third degree IMLS (open circles) using 501 symmetry distinct points.

Image of FIG. 3.
FIG. 3.

The rms error vs for L-IMLS. The results are for the fit (circles) and the fit (triangles). The filled symbols are for and the open ones for . The number of data points .

Image of FIG. 4.
FIG. 4.

The rms error at , 500, 750, 1000, 1500, and 2000 for L-IMLS using random (filled circles) and automatic point (open circles) selections. The straight lines are the least-squares fits of the data.

Image of FIG. 5.
FIG. 5.

The rms error at , 500, 750, 1000, 1500, 2000, 2500, and 3000 for L-IMLS for various degrees: (filled circles), (filled triangles), and (filled squares); and , , and (the corresponding open symbols). The straight lines are the least-squares fits of the data.

Image of FIG. 6.
FIG. 6.

The rms error vs fitting to the energy range for IMLS (filled symbols) and L-IMLS (open symbols). The results are for (circles), (triangles), and (squares) fits. The straight lines are the least-squares fits of the data.

Tables

Generic image for table
Table I.

The rms errors for various degrees of IMLS. The results demonstrate the improvement in accuracy by including high-order diagonal terms.

Generic image for table
Table II.

Comparison of accuracy of IMLS and L-IMLS.

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/content/aip/journal/jcp/127/21/10.1063/1.2805084
2007-12-05
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Interpolating moving least-squares methods for fitting potential energy surfaces: Improving efficiency via local approximants
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/21/10.1063/1.2805084
10.1063/1.2805084
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