Luigi Brugnano,Gianluca Frasca-Caccia,Felice Iavernaro et al.
Luigi Brugnano et al.
In this paper, we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The framework is based on an expansion of the vector field along an orthonormal basis, and relies o...
Randomized algorithms for distributed computation of principal component analysis and singular value decomposition [0.03%]
用于主成分分析和奇异值分解的分布式计算的随机算法
Huamin Li,Yuval Kluger,Mark Tygert
Huamin Li
Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a l...
Julio E Castrillón-Candás,Fabio Nobile,Raúl F Tempone
Julio E Castrillón-Candás
Consider a linear elliptic PDE defined over a stochastic stochastic geometry a function of N random variables. In many application, quantify the uncertainty propagated to a Quantity of Interest (QoI) is an important problem. The random doma...
C Campi,F Marchetti,E Perracchione
C Campi
We investigate the use of the so-called variably scaled kernels (VSKs) for learning tasks, with a particular focus on support vector machine (SVM) classifiers and kernel regression networks (KRNs). Concerning the kernels used to train the m...
Analytic regularity and stochastic collocation of high-dimensional Newton iterates [0.03%]
高维牛顿迭代的解析正则性和随机插值
Julio E Castrillón-Candás,Mark Kon
Julio E Castrillón-Candás
In this paper we introduce concepts from uncertainty quantification (UQ) and numerical analysis for the efficient evaluation of stochastic high dimensional Newton iterates. In particular, we develop complex analytic regularity theory of the...
Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons [0.03%]
凸多边形上关于Mean Value插值误差估计
Alexander Rand,Andrew Gillette,Chandrajit Bajaj
Alexander Rand
In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard f...
Andrew Gillette,Alexander Rand,Chandrajit Bajaj
Andrew Gillette
We prove the optimal convergence estimate for first order interpolants used in finite element methods based on three major approaches for generalizing barycentric interpolation functions to convex planar polygonal domains. The Wachspress ap...