Given N pairwise distinct and arbitrarily spaced points V_i in a domain of the x-y plane and N real numbers z_i, consider the problem of computing a C1 bivariate function F(x,y) whose values in V_i are exactly z_i. In this paper we present a method for solving the above problem, which is designed for extremely large data sets. A step of this method requires to minimize a quadratic functional; we prove that the hessian matrix is positive definite and is leading a P-regular splitting.
Galligani, Emanuele e Magnani, M. A.. "Surface fitting for extremely large scattered data sets" Working paper, Dipartimento di Matematica "Giuseppe Vitali", Università di Modena e Reggio Emilia, 2000. https://doi.org/10.25431/11380_593958
Surface fitting for extremely large scattered data sets
GALLIGANI, Emanuele;
2000
Abstract
Given N pairwise distinct and arbitrarily spaced points V_i in a domain of the x-y plane and N real numbers z_i, consider the problem of computing a C1 bivariate function F(x,y) whose values in V_i are exactly z_i. In this paper we present a method for solving the above problem, which is designed for extremely large data sets. A step of this method requires to minimize a quadratic functional; we prove that the hessian matrix is positive definite and is leading a P-regular splitting.
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