Constructing Positive Interpolatory Cubature Formulas

09/24/2020
by   Jan Glaubitz, et al.
0

Positive interpolatory cubature formulas (CFs) are constructed for quite general integration domains and weight functions. These CFs are exact for general vector spaces of continuous real-valued functions that contain constants. At the same time, the number of data points – all of which lie inside the domain of integration – and cubature weights – all positive – is less or equal to the dimension of that vector space. The existence of such CFs has been ensured by Tchakaloff in 1957. Yet, to the best of the author's knowledge, this work is the first to provide a procedure to successfully construct them.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

08/05/2021

Construction and application of provable positive and exact cubature formulas

Many applications require multi-dimensional numerical integration, often...
02/15/2021

Optimal quadrature formulas for computing of Fourier integrals in a Hilbert space

In the present paper the optimal quadrature formulas in the sense of Sar...
10/26/2021

Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matrices

We propose the use of the vector-valued distance to compute distances an...
03/05/2018

Positive Announcements

Arbitrary public announcement logic (APAL) reasons about how the knowled...
08/20/2021

Structure and Interleavings of Relative Interlevel Set Cohomology

The relative interlevel set cohomology (RISC) is an invariant of real-va...
01/03/2020

Monte-Carlo cubature construction

In numerical integration, cubature methods are effective, in particular ...
08/06/2020

Foundations of Reasoning with Uncertainty via Real-valued Logics

Real-valued logics underlie an increasing number of neuro-symbolic appro...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.