Scattered data interpolation in three or more variables
Mathematical methods in computer aided geometric design
Minimax models in the theory of numerical methods
Minimax models in the theory of numerical methods
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Object-oriented software for quadratic programming
ACM Transactions on Mathematical Software (TOMS)
Aggregation operators: properties, classes and construction methods
Aggregation operators
Interpolation of Lipschitz functions
Journal of Computational and Applied Mathematics
Citation-based journal ranks: The use of fuzzy measures
Fuzzy Sets and Systems
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This paper describes a new approach to multivariate scattered data smoothing. It is assumed that the data are generated by a Lipschitz continuous function f, and include random noise to be filtered out. The proposed approach uses known, or estimated value of the Lipschitz constant of f, and forces the data to be consistent with the Lipschitz properties of f. Depending on the assumptions about the distribution of the random noise, smoothing is reduced to a standard quadratic or a linear programming problem. We discuss an efficient algorithm which eliminates the redundant inequality constraints. Numerical experiments illustrate applicability and efficiency of the method. This approach provides an efficient new tool of multivariate scattered data approximation.