Zobrazeno 1 - 10
of 23
pro vyhledávání: '"Jantsch, Peter"'
Autor:
Guignard, Diane, Jantsch, Peter
Motivated by nonlinear approximation results for classes of parametric partial differential equations (PDEs), we seek to better understand so-called library approximations to analytic functions of countably infinite number of variables. Rather than a
Externí odkaz:
http://arxiv.org/abs/2210.07067
Autor:
Guignard, Diane, Jantsch, Peter
Publikováno v:
In Journal of Approximation Theory June 2024 300
Autor:
Bonito, Andrea, Cohen, Albert, DeVore, Ronald, Guignard, Diane, Jantsch, Peter, Petrova, Guergana
The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space $V_n$ which approximates well the solution manifold $\mathcal{M}$ consisting of all solutions $u(y)$ with $y$ the vector of para
Externí odkaz:
http://arxiv.org/abs/2005.02565
Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on Taylor exp
Externí odkaz:
http://arxiv.org/abs/1904.12105
This work focuses on weighted Lagrange interpolation on an unbounded domain, and analyzes the Lebesgue constant for a sequence of weighted Leja points. The standard Leja points are a nested sequence of points defined on a compact subset of the real l
Externí odkaz:
http://arxiv.org/abs/1606.07093
Autor:
Jackson, Michael A., Smith, Doug, Jantsch, Peter, Scurlock, Christina, Snyder, Chelsea, Fairchild, Eric, Mabe, Robin, Polaski, Emma
Polytope numbers for a given polytope are an integer sequence defined by the combinatorics of the polytope. Recent work by H. K. Kim and J. Y. Lee has focused on writing polytope number sequences as sums of simplex number sequences. We focus on $r$-r
Externí odkaz:
http://arxiv.org/abs/1507.01654
This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC approaches con
Externí odkaz:
http://arxiv.org/abs/1505.00680
A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data
Stochastic collocation methods for approximating the solution of partial differential equations with random input data (e.g., coefficients and forcing terms) suffer from the curse of dimensionality whereby increases in the stochastic dimension cause
Externí odkaz:
http://arxiv.org/abs/1404.2647
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