Algorithm 792

Algorithm 792: Accuracy tests of ACM algorithms for interpolation of scattered data in the plane We present results of accuracy tests on scattered-data fitting methods that have been published as ACM algorithms. The algorithms include seven triangulation-based methods and three modified Shepard methods, two of which are new algorithms. Our purpose is twofold: to guide potential users in the selection of an appropriate algorithm and to provide a test suite for assessing the accuracy of new methods (or existing methods that are not included in this survey). Our test suite consists of five sets of nodes, with node counts ranging from 25 to 100, and 10 test functions. These are made available in the form of three Fortran subroutines: TESTDT returns one of the node sets; TSTFN1 returns a value and, optionally, a gradient value, of one of the test functions; and TSTFN2 returns a value, first partials, and second partial derivatives of one of the test functions. (Source:

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 36 articles , 1 standard article )

Showing results 1 to 20 of 36.
Sorted by year (citations)

1 2 next

  1. Cavoretto, Roberto: Adaptive radial basis function partition of unity interpolation: a bivariate algorithm for unstructured data (2021)
  2. Dell’Accio, Francesco; Di Tommaso, Filomena; Nouisser, Otheman; Zerroudi, Benaissa: Fast and accurate scattered Hermite interpolation by triangular Shepard operators (2021)
  3. Nouisser, Otheman; Zerroudi, Benaissa: Modified Shepard’s method by six-points local interpolant (2021)
  4. Dell’Accio, Francesco; Di Tommaso, Filomena: On the hexagonal Shepard method (2020)
  5. Dell’Accio, Francesco; Di Tommaso, Filomena; Nouisser, Otheman; Siar, Najoua: Rational Hermite interpolation on six-tuples and scattered data (2020)
  6. Francomano, Elisa; Paliaga, Marta: A normalized iterative smoothed particle hydrodynamics method (2020)
  7. Occorsio, Donatella; Themistoclakis, Woula: Uniform weighted approximation on the square by polynomial interpolation at Chebyshev nodes (2020)
  8. Zheng, Sanpeng; Feng, Renzhong; Huang, Aitong: A modified moving least-squares suitable for scattered data fitting with outliers (2020)
  9. Cavoretto, Roberto; De Rossi, Alessandra; Dell’Accio, Francesco; Di Tommaso, Filomena: Fast computation of triangular Shepard interpolants (2019)
  10. Francomano, Elisa; Paliaga, Marta: The smoothed particle hydrodynamics method via residual iteration (2019)
  11. Dell’Accio, F.; Di Tommaso, F.; Nouisser, O.; Zerroudi, B.: Increasing the approximation order of the triangular Shepard method (2018)
  12. Francomano, E.; Paliaga, M.: Highlighting numerical insights of an efficient SPH method (2018)
  13. Biazar, Jafar; Hosami, Mohammad: An interval for the shape parameter in radial basis function approximation (2017)
  14. Dell’Accio, F.; Di Tommaso, F.: Bivariate Shepard-Bernoulli operators (2017)
  15. Erb, Wolfgang: Bivariate Lagrange interpolation at the node points of Lissajous curves -- the degenerate case (2016)
  16. Erb, Wolfgang; Kaethner, Christian; Ahlborg, Mandy; Buzug, Thorsten M.: Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves (2016)
  17. Rossini, Milvia; Volontè, Elena: Quasi-interpolation operators on hexagonal grids with high approximation orders in spaces of polyharmonic splines (2016)
  18. Jenkins, Thomas G.; Held, Eric D.: Coupling extended magnetohydrodynamic fluid codes with radiofrequency ray tracing codes for fusion modeling (2015)
  19. Bozzini, Mira; Rossini, Milvia: Properties of generators of quasi-interpolation operators of high approximation orders in spaces of polyharmonic splines (2014)
  20. Cavoretto, Roberto; De Rossi, Alessandra: A meshless interpolation algorithm using a cell-based searching procedure (2014)

1 2 next