On the existence of optimal affine methods for approximating linear functionals
Journal of Complexity
Scattered data interpolation in three or more variables
Mathematical methods in computer aided geometric design
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Minimax models in the theory of numerical methods
Minimax models in the theory of numerical methods
Curve and surface fitting with splines
Curve and surface fitting with splines
Optimal solution of nonlinear equations
Optimal solution of nonlinear equations
Fast Algorithm for the Cutting Angle Method of Global Optimization
Journal of Global Optimization
Global Optimization with Non-Convex Constraints - Sequential and Parallel Algorithms (Nonconvex Optimization and its Applications Volume 45) (Nonconvex Optimization and Its Applications)
Absorbent tuples of aggregation operators
Fuzzy Sets and Systems
Optimization Methods & Software
Design of embedded differential equation solver
International Journal of Intelligent Systems Technologies and Applications
Lipschitz continuity of triangular subnorms
Fuzzy Sets and Systems
| Hi-index | 7.29 |
This paper describes a new computational approach to multivariate scattered data interpolation. It is assumed that the data is generated by a Lipschitz continuous function f. The proposed approach uses the central interpolation scheme, which produces an optimal interpolant in the worst case scenario. It provides best uniform error bounds on f, and thus translates into reliable learning of f. This paper develops a computationally efficient algorithm for evaluating the interpolant in the multivariate case. We compare the proposed method with the radial basis functions and natural neighbor interpolation, provide the details of the algorithm and illustrate it on numerical experiments. The efficiency of this method surpasses alternative interpolation methods for scattered data.