eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-12-02
9391
1
23
10.4230/DagSemProc.09391.1
article
09391 Abstracts Collection – Algorithms and Complexity for Continuous Problems
Müller-Gronbach, Thomas
Plaskota, Leszek
Traub, Joseph F.
From 20.09.09 to 25.09.09, the Dagstuhl Seminar 09391
Algorithms and Complexity for Continuous Problems was held in the
International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, participants presented their current research, and
ongoing work and open problems were discussed. Abstracts of the
presentations given during the seminar are put together in this paper. The
first section describes the seminar topics and goals in general. Links to
extended abstracts or full papers are provided, if available.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09391/DagSemProc.09391.1/DagSemProc.09391.1.pdf
Computational complexity of continuous problems
partial information
high-dimensional problems
tractability analysis
quasi-Monte Carlo methods
op operator equations
non-linear approximation
stochastic computation
ill posed-problems
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-12-02
9391
1
4
10.4230/DagSemProc.09391.2
article
Discrepancy Bounds for Mixed Sequences
Gnewuch, Michael
A mixed sequence is a sequence in the $s$-dimensional unit cube
which one obtains by concatenating a $d$-dimensional low-discrepancy
sequence with an $s-d$-dimensional random sequence.
We discuss some probabilistic bounds on the star discrepancy of
mixed sequences.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09391/DagSemProc.09391.2/DagSemProc.09391.2.pdf
Star Discrepancy
Mixed Sequence
Hybrid Method
Monte Carlo
Quasi-Monte Carlo
Probabilistic Bounds
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-12-02
9391
1
19
10.4230/DagSemProc.09391.3
article
Evaluating Expectations of Functionals of Brownian Motions: a Multilevel Idea
Hickernell, Fred J.
Müller-Gronbach, Thomas
Niu, Ben
Ritter, Klaus
Prices of path dependent options may be modeled as expectations of functions of an infinite sequence of real variables. This talk presents recent work on bounding the error of such expectations using quasi-Monte Carlo algorithms. The expectation is approximated by an average of $n$ samples, and the functional of an infinite number of variables is approximated by a function of only $d$ variables. A multilevel algorithm employing a sum of sample averages, each with different truncated dimensions, $d_l$, and different sample sizes, $n_l$, yields faster convergence than a single level algorithm. This talk presents results in the worst-case error setting.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09391/DagSemProc.09391.3/DagSemProc.09391.3.pdf
Brownian motions
multilevel
option pricing
worst-case error
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-12-02
9391
1
19
10.4230/DagSemProc.09391.4
article
Quasi-Monte Carlo, Monte Carlo, and regularized gradient optimization methods for source characterization of atmospheric releases
Sikorski, Krzysztof
Addepalli, Bhagirath
Pardyjak, E. R.
Zhdanov, M.
An inversion technique based on MC/QMC search and regularized gradient optimization was developed to solve the atmospheric source characterization problem. The Gaussian Plume Model was adopted as the forward operator and QMC/MC search was implemented in order to find good starting points for the gradient optimization. This approach was validated on the Copenhagen Tracer Experiments. The QMC approach with the utilization of clasical and scrambled Halton, Hammersley and Sobol points was shown to be 10-100 times more efficient than the Mersenne Twister Monte Carlo generator. Further experiments are needed for different data sets. Computational complexity analysis needs to be
carried out .
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09391/DagSemProc.09391.4/DagSemProc.09391.4.pdf
Atmospheric source problem
Gaussian Plume Model
Quasi Monte Carlo method
gradient optimization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-12-02
9391
1
9
10.4230/DagSemProc.09391.5
article
Weighted L_2 B Discrepancy and Approximation of Integrals over Reproducing Kernel Hilbert Spaces
Gnewuch, Michael
We extend the notion of $L_2$ $B$ discrepancy provided in
[E. Novak, H. Wo'zniakowski, $L_2$ discrepancy and multivariate
integration, in: Analytic number theory. Essays in honour of Klaus
Roth. W. W. L. Chen, W. T. Gowers, H. Halberstam, W. M. Schmidt,
and R. C. Vaughan (Eds.), Cambridge University Press, Cambridge,
2009, 359 – 388] to the weighted $L_2$ $mathcal{B}$ discrepancy.
This newly defined notion allows to
consider weights, but also volume measures different from the Lebesgue
measure and classes of test sets different from measurable subsets
of some Euclidean space.
We relate the weighted $L_2$ $mathcal{B}$ discrepancy to numerical
integration defined over weighted reproducing kernel Hilbert spaces
and settle in this way an open problem posed by Novak and
Wo'zniakowski.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09391/DagSemProc.09391.5/DagSemProc.09391.5.pdf
Discrepancy
Numerical Integration
Quasi-Monte Carlo
Reproducing Kernel Hilbert Space