Radial basis function interpolation in the quantum trajectory method: optimization of the multi-quadric shape parameter.
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Publication:1873355
DOI10.1016/S0021-9991(02)00046-3zbMath1040.81515OpenAlexW2087444559MaRDI QIDQ1873355
Robert E. Wyatt, Corey J. Trahan
Publication date: 20 May 2003
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0021-9991(02)00046-3
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Software, source code, etc. for problems pertaining to quantum theory (81-04)
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Uses Software
Cites Work
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- Interpolation of scattered data: distance matrices and conditionally positive definite functions
- Theory and applications of the multiquadric-biharmonic method. 20 years of discovery 1968-1988
- Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
- Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation
- Interpolation of track data with radial basis methods
- A contribution of the multiquadric method: Interpolation of potential inside the Earth
- Improved accuracy of multiquadric interpolation using variable shape parameters
- Miscellaneous error bounds for multiquadric and related interpolators
- Sparse approximate multiquadric interpolation
- Lower bounds for norms of inverses of interpolation matrices for radial basis functions
- Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations
- Adaptive greedy techniques for approximate solution of large RBF systems
- A unified theory of radial basis functions. Native Hilbert spaces for radial basis functions. II
- Meshless methods based on collocation with radial basis functions
- Local, point-wise rotational transformations of the conservation equations into stream-wise coordinates.
- Multivariate radial basis interpolation for solving quantum fluid dynamical equations
- Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
- Error estimates and condition numbers for radial basis function interpolation
- Approximation by radial basis functions with finitely many centers
- A boundary element scheme for diffusion problems using compactly supported radial basis functions
- An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation
- The parameter \(R^ 2\) in multiquadric interpolation
- Scattered Data Interpolation: Tests of Some Method
- Improved error bounds for scattered data interpolation by radial basis functions
- A new class of radial basis functions with compact support
- Multivariate Interpolation and Conditionally Positive Definite Functions. II
- A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I
- The elements of statistical learning. Data mining, inference, and prediction
- Recent progress in multivariate approximation. Proceedings of the 4th international conference, Witten-Bommerholz, Germany, Septembe 24--29, 2000
- Hardy's multiquadric-biharmonic method for gravity field predictions. II