In this paper, we present a method for the numerical differentiation of bivariate functions when a set of noisy data is given. We suppose we have a sample coming from an independent process with unknown covariance matrix. We construct the gradient estimator using a multiresolution analysis and the usual difference operators. The asymptotic properties of the estimator are studied and convergence results are provided. The method is suitable for any data configuration. (C) 2003 Elsevier Science Ltd. All rights reserved
Bozzini, M., Rossini, M. (2003). Numerical differentiation of 2D functions from noisy data. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 45(1-3), 309-327 [10.1016/S0898-1221(03)80021-4].
Numerical differentiation of 2D functions from noisy data
BOZZINI, MARIA TUGOMIRA;ROSSINI, MILVIA FRANCESCA
2003
Abstract
In this paper, we present a method for the numerical differentiation of bivariate functions when a set of noisy data is given. We suppose we have a sample coming from an independent process with unknown covariance matrix. We construct the gradient estimator using a multiresolution analysis and the usual difference operators. The asymptotic properties of the estimator are studied and convergence results are provided. The method is suitable for any data configuration. (C) 2003 Elsevier Science Ltd. All rights reserved
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