A review on acoustic reconstruction of temperature profiles: From time measurement to reconstruction algorithm
Acoustic tomography is a technique widely used in nonintrusive temperature measurement.
The time of flight (TOF) of acoustic waves can be used to estimate the temperatures of a …
The time of flight (TOF) of acoustic waves can be used to estimate the temperatures of a …
The numerical approximation of nonlinear functionals and functional differential equations
D Venturi - Physics Reports, 2018 - Elsevier
The fundamental importance of functional differential equations has been recognized in
many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional …
many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional …
Adaptive Leja sparse grid constructions for stochastic collocation and high-dimensional approximation
We propose an adaptive sparse grid stochastic collocation approach based upon Leja
interpolation sequences for approximation of parameterized functions with high-dimensional …
interpolation sequences for approximation of parameterized functions with high-dimensional …
Computing multivariate Fekete and Leja points by numerical linear algebra
We discuss and compare two greedy algorithms that compute discrete versions of Fekete-
like points for multivariate compact sets by basic tools of numerical linear algebra. The first …
like points for multivariate compact sets by basic tools of numerical linear algebra. The first …
The Sparse Grids Matlab kit--a Matlab implementation of sparse grids for high-dimensional function approximation and uncertainty quantification
The Sparse Grids Matlab Kit provides a Matlab implementation of sparse grids, and can be
used for approximating high-dimensional functions and, in particular, for surrogate-model …
used for approximating high-dimensional functions and, in particular, for surrogate-model …
Small errors imply large evaluation instabilities
R Schaback - Advances in Computational Mathematics, 2023 - Springer
Numerical analysts and scientists working in applications often observe that once they
improve their techniques to get a better accuracy, some instability of the evaluation creeps in …
improve their techniques to get a better accuracy, some instability of the evaluation creeps in …
Bivariate polynomial interpolation on the square at new nodal sets
As known, the problem of choosing “good” nodes is a central one in polynomial
interpolation. While the problem is essentially solved in one dimension (all good nodal …
interpolation. While the problem is essentially solved in one dimension (all good nodal …
Convergence of sparse collocation for functions of countably many Gaussian random variables (with application to elliptic PDEs)
We give a convergence proof for the approximation by sparse collocation of Hilbert-space-
valued functions depending on countably many Gaussian random variables. Such functions …
valued functions depending on countably many Gaussian random variables. Such functions …
A dynamically adaptive sparse grids method for quasi-optimal interpolation of multidimensional functions
In this work we develop a dynamically adaptive sparse grids (SG) method for quasi-optimal
interpolation of multidimensional analytic functions defined over a product of one …
interpolation of multidimensional analytic functions defined over a product of one …
[HTML][HTML] On the Lebesgue constant of Leja sequences for the complex unit disk and of their real projection
MA Chkifa - Journal of Approximation Theory, 2013 - Elsevier
We consider Leja sequences of points for polynomial interpolation on the complex unit disk
U and the corresponding sequences for polynomial interpolation on the real interval [− 1, 1] …
U and the corresponding sequences for polynomial interpolation on the real interval [− 1, 1] …