Publications |
Randomized Complexity of Mean Computation and the Adaption Problem
-
[preprint]
- see also
http://arxiv.org/abs/2401.14100
Randomized Complexity of Parametric Integration and the Role of Adaption II. Sobolev Spaces
-
J. Complexity 82 (2024), 101823.
[preprint]
- see also
http://arxiv.org/abs/2306.13499
Randomized Complexity of Vector-Valued Approximation
- to appear in: A. Hinrichs, P. Kritzer, F. Pillichshammer (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2022, Springer-Verlag. [preprint]
- see also
http://arxiv.org/abs/2306.13697
Randomized Complexity of Parametric Integration and the Role of Adaption I. Finite Dimensional Case
-
J. Complexity 82 (2024), 101821.
[preprint]
- see also
http://arxiv.org/abs/2306.13471
Lower bounds for the number of random bits in Monte Carlo algorithms
-
In: Keller, A. (ed) Monte Carlo and Quasi-Monte Carlo Methods. MCQMC 2020. Springer Proceedings in Mathematics & Statistics, vol 387, pp.131-147, Springer, 2022.
[preprint]
- see also
http://arxiv.org/abs/2012.12774
On the power of restricted Monte Carlo algorithms
- 2018 MATRIX Annals, Springer, 2020, pp. 45--59. [preprint]
Complexity of stochastic integration in Sobolev classes
- J. Math. Anal. Appl. 476 (2019), 177-195 [preprint]
On the complexity of computing the Lq norm
- J. Complexity 49 (2018), 1-26 [preprint]
Lower complexity bounds for parametric stochastic Itô integration
-
Monte Carlo and quasi-Monte Carlo methods, MCQMC 2016. Proceedings of the 12th international conference on `Monte Carlo and quasi-Monte Carlo methods in scientific computing', Stanford, CA, August 14-19, 2016 ( A. B. Owen, P. W. Glynn, eds.),
Springer Proceedings in Mathematics & Statistics 241, pp. 295-312, Berlin 2018 [preprint]
On the complexity of parametric ODEs and related problems
- Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan (J. Dick, F. Y. Kuo, H. Wozniakowski, Eds.), pp. 567-595, Springer, Berlin, 2018 [preprint]
Complexity of Banach space valued and parametric stochastic Itô integration
- with Th. Daun
- J. Complexity 40 (2017), 100-122 [preprint]
Complexity of parametric initial value problems
for systems of ODEs - with Th. Daun
- Mathematics and Computers in Simulation 135, 72-85 (May 2017), doi:10.1016/j.matcom.2015.04.008 [preprint]
Complexity of parametric integration in various smoothness classes - with Th. Daun
- J. Complexity 30, No. 6, 750-766 (2014). [preprint]
Complexity of parametric initial value problems in Banach spaces - with Th. Daun
- J. Complexity 30, No. 4, 392-429 (2014). [preprint]
On the randomized complexity of Banach space valued integration - with A. Hinrichs
- Studia Math. 223, 205-215 (2014). [preprint]
Complexity of initial value problems in Banach spaces
- J. Math. Phys. Anal.
Geom. 9, 73-101 (2013). [preprint]
Complexity of Banach space valued and parametric integration - with Th. Daun
- Monte Carlo and Quasi-Monte Carlo Methods 2012 (J. Dick, F. Y. Kuo, G. W. Peters, I. H. Sloan, eds.), Springer Proceedings in Mathematics and Statistics 65, pp. 297-316, Berlin, 2013. [preprint]
Stochastic approximation of functions and applications
- L. Plaskota, H. Wozniakowski (ed.), Monte Carlo and Quasi-Monte Carlo Methods
2010, Selected papers based on the presentations at the 9th international
conference on Monte Carlo and quasi Monte Carlo methods in scientific
computing, Warsaw, Poland, August 15--20, 2010,
Springer Proceedings in Mathematics & Statistics 23, pp. 95-131, Berlin, 2012 . [preprint]
Ultrastability of n-th minimal errors
- J. Complexity 28, No. 4, 440-458 (2012) . [preprint]
The randomized complexity of indefinite integration - with B. Milla
- J. Complexity 27, No. 3-4, 352-382 (2011) . [preprint]
- Randomized
approximation of Sobolev embeddings. III.
- J.
Complexity 25, No. 5, 473-507 (2009). [preprint]
- Randomized
approximation of Sobolev embeddings. II.
- J.
Complexity 25, No. 5, 455-472 (2009). [preprint]
- The
randomized complexity of initial value problems
- with B. Milla
- Journal
of
Complexity 24, No. 2, 77-88 (2008) [preprint]
- Randomized
approximation of
Sobolev embeddings
- Keller,
Alexander (ed.) et al., Monte Carlo and quasi-Monte
Carlo methods 2006. Selected papers based on the presentations at the
7th international conference `Monte Carlo and quasi-Monte Carlo methods
in scientific computing', Ulm, Germany, August 14--18, 2006. Berlin:
Springer. 445-459 (2008) [preprint]
- Quantum
lower bounds by entropy numbers
- J.
Complexity 23, No. 4-6, 793-801 (2007) Abstract and paper avaibable at
http://arXiv.org/abs/quant-ph/0611294
- Numerical
analysis on a quantum computer
- Lirkov,
Ivan (ed.) et al., Large-scale scientific computing. 5th international
conference, LSSC 2005, Sozopol, Bulgaria, June 6--10, 2005. Revised
papers. Berlin: Springer. Lecture Notes in Computer Science 3743, 28-39
(2006)
[preprint]
- The quantum
query complexity of elliptic PDE
- J.
Complexity 22, No. 5, 691-725 (2006) Abstract and paper avaibable at
http://arXiv.org/abs/quant-ph/0512241
- The
randomized information complexity of elliptic PDE
- J.
Complexity 22, No. 2, 220--249 (2006) [preprint]
- Monte Carlo
Approximation of weakly singular integral operators
- J.
Complexity 22, No. 2, 192--219 (2006) [preprint]
- Quantum
Complexity of Numerical Problems
- Cucker,
Felipe (ed.) et al., Foundations of computational mathematics:
Minneapolis 2002 (FoCM 2002). Selected papers based on the plenary
talks presented at FoCM 2002, Minneapolis, MN, USA, August 5--14, 2002.
Cambridge: Cambridge University Press. London Mathematical Society
Lecture Note Series 312, 76-95 (2004) [preprint]
- On the
Power
of Quantum Algorithms
for Vector Valued Mean Computation
- Paper
submitted to: Monte
Carlo Methods and Applications. Abstract and paper avaibable at http://arXiv.org/abs/quant-ph/0403109
- Quantum
Approximation I.
Embeddings of Finite Dimensional L_p Spaces
- Journal
of
Complexity 20
(2004), 5-26. Abstract and paper avaibable at http://arXiv.org/abs/quant-ph/0305030
- Quantum
Approximation II.
Sobolev Embeddings
- Journal
of
Complexity 20
(2004) 27-45. Abstract and paper avaibable at http://arXiv.org/abs/quant-ph/0305031
- Quantum
Boolean Summation
with Repetitions in the Worst-Average Setting
- with M. Kwas
and
H. Wozniakowski
- In: Monte
Carlo and Quasi-Monte
Carlo Methods 2002 (H. Niederreiter, Ed.), pp. 243-258,
Springer-Verlag,
2004.
- [ps] [pdf]
- How Many
Random Bits Do We
Need for Monte Carlo Integration?
- with E.
Novak
and H. Pfeiffer
- In: Monte
Carlo and Quasi-Monte
Carlo Methods 2002 (H. Niederreiter, Ed.), pp. 27-49, Springer-Verlag,
2004.
- [ps] [pdf]
- Quantum
Integration in Sobolev
Classes
- Journal
of
Complexity 19
(2003), 19-42. Abstract and paper avaibable at http://arXiv.org/abs/quant-ph/0112153
- From
Monte
Carlo to Quantum
Computation
- Proceedings
of the 3rd IMACS
Seminar on Monte Carlo Methods MCM2001, Salzburg, Special Issue of
Mathematics
and Computers in Simulation (Guest Eds.: K. Entacher, W. Ch. Schmid, A.
Uhl) 62 (2003), 219--230.
- [ps] [pdf]
- On a
Problem
in Quantum Summation
- with E. Novak
- Journal
of
Complexity 19
(2003), 1-18. Abstract and paper avaibable at http://arXiv.org/abs/quant-ph/0109038
- Optimal
Quadrature for Haar
Wavelet Spaces
- with F. J.
Hickernell and R.-X.
Yue
- Math.
Comput.
73 No. 245
(2004), 259-277.
- [ps] [pdf]
- Quantum
Summation with an
Application to Integration
- Journal
of
Complexity 18
(2002), 1-50. Abstract and paper avaibable at http://arXiv.org/abs/quant-ph/0105116
- Optimal
Summation and Integration
by Deterministic, Randomized, and Quantum Algorithms
- with E. Novak
- in:
K.-T. Fang,
F. J. Hickernell, H. Niederreiter (Eds.), Monte Carlo and Quasi-Monte
Carlo
Methods 2000, Springer-Verlag, Berlin, 2002, pp. 50--62. Abstract and
paper
avaibable at http://arXiv.org/abs/quant-ph/0105114
Multilevel
Monte Carlo methods - Margenov,
S. (ed.) et al., Large-scale scientific computing. 3rd international
conference,
- LSSC 2001,
Sozopol, Bulgaria, June 6-10, 2001. Revised papers. Berlin: Springer.
- Lect. Notes
Comput. Sci. 2179, 58-67 (2001) [preprint]
The inverse
of the star-discrepancy
depends linearly on the dimension - with E.
Novak,
G. W. Wasilkowski,
H. Wozniakowski
- Acta
Arithmetica XCVI.3 (2001),
279-302
[preprint]
- The
multilevel method of
dependent tests
- Advances
in
Stochastic Simulation
Methods (N. Balakrishnan,V.B. Melas, S. Ermakov, editors), pp. 47-62.
Birkhäuser,
Boston, Basel, Berlin, 2000. [preprint]
- Variance
reduction by means
of deterministic computation: Collision estimate
- J.
Statist.
Planning and
Inference 85 (2000), 159-169 [preprint]
- Monte
Carlo
complexity of
parametric integration
- with E.
Sindambiwe
- J.
Complexity 15 (1999),
317-341
[preprint]
- Wavelet
Monte
Carlo methods
for the global solution of integral equations
- Proceedings
of the Third
International Conference on Monte Carlo and Quasi-Monte Carlo Methods,
Claremont 1998 (H. Niederreiter and J. Spanier, editors), pp. 227 -
237,
Springer 1999 [preprint]
- Monte
Carlo
complexity of
global solution of integral equations
- J.
Complexity
14, No.2, 151-175
(1998). [preprint]
- A
multilevel
version of the
method of dependent tests
- Proceedings
of the 3rd St.
Petersburg Workshop on Simulation, S. M. Ermakov, Y. N. Kashtanov and
V.
B. Melas, editors, pp. 31 - 35, St. Petersburg University Press, 1998
- Computing
discrepancies related
to spaces of smooth periodic functions
- with K. Frank
- Niederreiter,
Harald (ed.)
et al., Monte Carlo and quasi-Monte Carlo methods 1996. Proceedings of
a conference at the University of Salzburg, Austria, July 9-12, 1996.
Berlin:
Springer. Lect. Notes Stat., Springer-Verlag. 127, 238-250 (1997).
- Using the
Galerkin method
for variance reduction
- in:
"Mathematical methods
in stochastic simulation and experimental design", Proceedings of the
Second
St. Petersburg Workshop on Simulation, Publishing House of Saint
Petersburg
University, 1996, pp. 56 - 59
- Computing
discrepancies of
Smolyak quadrature rules
- with K. Frank
- J.
Complexity
12, No.4, 287-314
(1996).
- Information
complexity of
multivariate Fredholm integral equations in Sobolev classes
- with K.
Frank
and S. Pereverzev
- J.
Complexity
12, No.1, 17-34
(1996).
- Complexity
theory of Monte
Carlo algorithms
- Renegar,
James (ed.) et al.,
The mathematics of numerical analysis. 1995 AMS-SIAM summer seminar in
applied mathematics, July 17 - August 11, 1995, Park City, UT, USA.
Providence,
RI: American Mathematical Society. Lect. Appl. Math. 32, 405-419 (1996).
- Efficient
algorithms for
computing the $L_2$-discrepancy
- Math.
Comput.
65, No.216,
1621-1633 (1996).
- Variance
reduction for Monte
Carlo methods by means of deterministic numerical computation.
- Monte
Carlo
Methods Appl.
1, No.4, 251-277 (1995).
- Complexity
of
local solution
of integral equations
- with K. Frank
- Schock,
Eberhard (ed.), Beiträge
zur Angewandten Analysis und Informatik. Helmut Brakhage zu Ehren.
Aachen:
Shaker Verlag. Berichte aus der Mathematik. 55-68 (1994).
- The Monte
Carlo complexity
of Fredholm integral equations
- with P.
Mathé
- Math.
Comput.
60, No.201,
257-278 (1993).
- Random
approximation in numerical
analysis
- Bierstedt,
Klaus D. (ed.)
et al., Functional analysis. Proceedings of the Essen Conference, held
in Essen, Germany, November 24 - 30, 1991. New York, NY: Dekker. Lect.
Notes Pure Appl. Math. 150, 123-171 (1993).
- Complexity
of
integral equations
and relations to $s$-numbers
- J.
Complexity
9, No.1, 141-153
(1993).
- Lower
bounds
for the complexity
of Monte Carlo function approximation
- J.
Complexity
8, No.3, 277-300
(1992).
- Efficiency
of
Monte Carlo
algorithms in numerical analysis
- Budach,
Lothar (ed.), Fundamentals
of computation theory. 8th international conference, FCT '91, Gosen,
Germany,
September 9-13, 1991. Proceedings. Berlin etc.: Springer-Verlag. Lect.
Notes Comput. Sci. 529, 33-44 (1991).
- Parallel
information-based
complexity
- with J.-D.
Kern
- J.
Complexity
7, No.4, 339-370
(1991).
- Corrections
to "Probabilistic
analysis of numerical methods for integral equations"
- J.
Integral
Equations Appl.
3, No.3, 469-472 (1991).
- Probabilistic
analysis of
numerical methods for integral equations
- J.
Integral
Equations Appl.
3, No.2, 289-319 (1991).
- Probabilistic
complexity
analysis for linear problems in bounded domains
- J.
Complexity
6, No.3, 231-255
(1990).
- Invertibility
of random Fredholm
operators
- Stochastic
Anal. Appl. 8,
No.1, 1-59 (1990).
- On the
relation between linear
n-widths and approximation numbers
- J.
Approximation Theory 58,
No.3, 315-333 (1989).
- s-numbers
of integral operators
with Hölder continuous kernels over metric compacta
- with B.
Carl
and T. Kühn
- J. Funct.
Anal. 81, No.1,
54-73 (1988).
- A note on
elementary equivalence
of C(K) spaces
- with C.
Henson
and L. Moore
jun.
- J. Symb.
Logic 52, 368-373
(1987).
- Banach
space
model theory.
II: Isomorphic equivalence
- with C.
Henson
- Math.
Nachr.
125, 301-317
(1986).
- The
uniform
classification
of boundedly compact locally convex spaces
- Czech.
Math.
J. 36(111),
68-71 (1986).
- Elementary
equivalence of
$C_\sigma(K)$ spaces for totally disconnected, compact Hausdorff K
- with C.
Henson
and L. Moore
jun.
- J. Symb.
Logic 51, 135-146
(1986).
- On the
optimal error of degenerate
kernel methods
- J.
Integral
Equations 9,
No.3, 251-266 (1985).
- Ultrapowers
of locally convex
spaces and applications II
- Math.
Nachr.
121, 211-229
(1985).
- Embedding
maps between Hölder
spaces over metric compacta and eigenvalues of integral operators
- with T.
Kühn
- Indagationes
Math. 47, 47-62
(1985).
- On the
asymptotic behaviour
of Hilbert numbers
- with R.
Linde
- Math.
Nachr.
119, 117-120
(1984).
- Ultrapowers
of locally convex
spaces and applications I
- Math.
Nachr.
118, 285-315
(1984).
- A problem
in
discretization
theory related to the approximation property of Banach spaces
- Math.
Nachr.
111, 147-152
(1983).
- Elementary
equivalence of
$L_1$-preduals
- with C.W.
Henson and L.C.jun.
Moore
- Banach
space
theory and its
applications, Proc. 1st Romanian-GDR Semin., Bucharest 1981, Lect.
Notes
Math. 991, 79-90 (1983).
- Some open
problems in the
nonlinear classification of Banach spaces
- with P.
Mankiewicz
- Banach
space
theory and its
applications, Proc. 1st Romanian-GDR Semin., Bucharest 1981, Lect.
Notes
Math. 991, 91-95 (1983).
- The
isomorphic problem of
envelopes
- Stud.
Math.
73, 41-49 (1982).
- Applications
of ultrapowers
to the uniform and Lipschitz classification of Banach spaces
- with P.
Mankiewicz
- Stud.
Math.
73, 225-251 (1982).
- Order
bounded
operators and
tensor products of Banach lattices
- with N.J.
Nielsen and G.H.
Olsen
- Math.
Scand.
49, 99-127 (1981).
- Ultraproducts
of $L_1$-predual
spaces
- Fundam.
Math.
113, 221-234
(1981).
- Finite
representability and
super-ideals of operators
- Diss.
Math.
172, 37 P. (1980).
- Closed
operator ideals and
interpolation
- J. Funct.
Anal. 35, 397-411
(1980).
- Ultraproducts
in Banach space
theory
- J. Reine
Angew. Math. 313,
72-104 (1980).
- A
characterization of $(\infty,p,q)$-integral
operators
- with A.
Pietsch
- Math.
Nachr.
89, 197-202
(1979).
- Finite
representability of
operators
- Operator
algebras, ideals,
and their applications in theoretical physics, Proc. int. Conf. Leipzig
1977, 33-39 (1978).
- Some
properties of operator
spaces
- Serdica
3,
168-175 (1977).
- Weak
sequential completeness
of Banach operator ideals
- Sib.
Math. J.
17, 857-862
(1977).
- Linear-topological
properties
of operator spaces
- Gen.
Topol.
Relat. mod. Anal.
Algebra, Proc. 4th Prague Topol. Symp. 1976, Part B, 156-158 (1977).
- Strongly
exposed and conical
points in the projective tensor product (Russian)
- Teor.
Funkts., Funkts. Anal.
Prilozh. 22, 146-154 (1975).
- Approximation
properties
in tensor products
- Math.
Notes
17, 269-272 (1975).
translation from Mat. Zametki 17, 459-466 (1975).
- The
differentiability of
the norm in spaces of operators
- Funct.
Anal.
Appl. 9, 360-362
(1975); translation from Funkts. Anal. Prilozh. 9, No.4, 93-94 (1974).
- The
reflexivity of the Banach
space L(E,F)
- Funct.
Anal.
Appl. 8, 186-187
(1974); translation from Funkts. Anal. Prilozh. 8, No.2, 97-98 (1974).
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