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Differentiation by integration with Jacobi polynomials
Numerical differentiation Ill-pose problems Jacobi orthogonal polynomials Orthogonal series
2011/2/28
In this paper, the numerical differentiation by integration method based on Jacobi polynomials originally introduced by Mboup, Fliess and Join [20, 21] is revisited in the central case where the used ...
Applications of the quadratic covariation differentiation theory: variants of the Clark-Ocone and Stroock's formulas
the quadratic covariation differentiation theory the Clark-Ocone and Stroock's formulas
2010/11/11
In a 2006 article (\cite{A1}), Allouba gave his quadratic covariation differentiation theory for It\^o's integral calculus. He defined the derivative of a semimartingale with respect to a Brownian mo...
Higher-order derivatives of the QR and of the real symmetric eigenvalue decomposition in forward and reverse mode algorithmic differentiation
univariate Taylor polynomial arithmetic higher-order derivatives QR decomposition real symmetric eigenvalue decomposition
2010/12/15
We address the task of higher-order derivative evaluation of computer programs that contain QR
decompositions and real symmetric eigenvalue decompositions. The approach is a combination of univariate...