Gaussian kernel quadrature at scaled Gauss–Hermite nodes
نویسندگان
چکیده
منابع مشابه
Gaussian Quadrature for Kernel Features
Kernel methods have recently attracted resurgent interest, showing performance competitive with deep neural networks in tasks such as speech recognition. The random Fourier features map is a technique commonly used to scale up kernel machines, but employing the randomized feature map means that O(ε-2) samples are required to achieve an approximation error of at most ε. We investigate some alter...
متن کاملGaussian rational quadrature formulas for ill-scaled integrands
A flexible treatment of Gaussian quadrature formulas based on rational functions is given to evaluate the integral ∫ I f(x)W (x)dx, when f is meromorphic in a neighborhood V of the interval I and W (x) is an ill-scaled weight function. Some numerical tests illustrate the power of this approach in comparison with Gautschi’s method.
متن کاملWeighted quadrature rules with binomial nodes
In this paper, a new class of a weighted quadrature rule is represented as -------------------------------------------- where is a weight function, are interpolation nodes, are the corresponding weight coefficients and denotes the error term. The general form of interpolation nodes are considered as that and we obtain the explicit expressions of the coefficients using the q-...
متن کاملFully symmetric kernel quadrature
Kernel quadratures and other kernel-based approximation methods typically suffer from prohibitive cubic time and quadratic space complexity in the number of function evaluations. The problem arises because a system of linear equations needs to be solved. In this article we show that the weights of a kernel quadrature rule can be computed efficiently and exactly for up to tens of millions of nod...
متن کاملAnti-Gaussian quadrature formulas
An anti-Gaussian quadrature formula is an (n+ 1)-point formula of degree 2n− 1 which integrates polynomials of degree up to 2n+ 1 with an error equal in magnitude but of opposite sign to that of the n-point Gaussian formula. Its intended application is to estimate the error incurred in Gaussian integration by halving the difference between the results obtained from the two formulas. We show tha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: BIT Numerical Mathematics
سال: 2019
ISSN: 0006-3835,1572-9125
DOI: 10.1007/s10543-019-00758-3