# A Universal Algorithm for Multivariate Integration

A Universal Algorithm for Multivariate Integration We present an algorithm for multivariate integration over cubes that is unbiased and has optimal order of convergence (in the randomized sense as well as in the worst-case setting) for all Sobolev spaces $${H^{r,\mathrm{mix}}([0,1]^d)}$$ H r , mix ( [ 0 , 1 ] d ) and $${H^s([0,1]^d)}$$ H s ( [ 0 , 1 ] d ) for $$s>d/2$$ s > d / 2 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Foundations of Computational Mathematics Springer Journals

# A Universal Algorithm for Multivariate Integration

, Volume 17 (4) – Feb 18, 2016
22 pages

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Publisher
Springer Journals
Copyright
Copyright © 2016 by SFoCM
Subject
Mathematics; Numerical Analysis; Economics, general; Applications of Mathematics; Linear and Multilinear Algebras, Matrix Theory; Math Applications in Computer Science; Computer Science, general
ISSN
1615-3375
eISSN
1615-3383
D.O.I.
10.1007/s10208-016-9307-y
Publisher site
See Article on Publisher Site

### Abstract

We present an algorithm for multivariate integration over cubes that is unbiased and has optimal order of convergence (in the randomized sense as well as in the worst-case setting) for all Sobolev spaces $${H^{r,\mathrm{mix}}([0,1]^d)}$$ H r , mix ( [ 0 , 1 ] d ) and $${H^s([0,1]^d)}$$ H s ( [ 0 , 1 ] d ) for $$s>d/2$$ s > d / 2 .

### Journal

Foundations of Computational MathematicsSpringer Journals

Published: Feb 18, 2016

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