Erich Novak: Publications

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104) With Henryk Wozniakowski: Tractability of multivariate problems for standard and linear information in the worst case setting: Part II,
submitted 11/2016, to appear in:
Contemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan, Josef Dick, Frances Y. Kuo, Henryk Wozniakowski (eds.),
Springer Verlag, 2018.
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103) With Shun Zhang: Optimal Quadrature Formulas for the Sobolev Space $H^1$,
submitted manuscript, 09/2016
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J. of Scientific Computing 78, 2019, 274--289.

102) With Aicke Hinrichs, Mario Ullrich and Henryk Wozniakowski: Product rules are optimal for numerical integration in classical smoothness spaces,
submitted manuscript, 03/2016.
Journal of Complexity 38 (2017), 39--49.
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101) With Mario Ullrich, Henryk Wozniakowski and Shun Zhang: Complexity of Oscillatory Integrals on the Real Line,
submitted manuscript, 11/2015
Adv. in Comput. Math. 43 (2017), 537--553.
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100) With David Krieg: A Universal Algorithm for Multivariate Integration,
submitted manuscript, 07/2015
Found. of Comput. Math. 17 (2017), 895--916.
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99) With Henryk Wozniakowski: Tractability of multivariate problems for standard and linear information in the worst case setting: Part I.
submitted manuscript, 03/2015
J. Approx. Th. 207 (2016), 177--192.
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98) Some Results on the Complexity of Numerical Integration
submitted manuscript, 09/2014
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In: Monte Carlo and Quasi-Monte Carlo Methods, MCQMC, Leuven, Belgium, Ronald Cools and Dirk Nuyens (eds.), Springer 2016.
97) With Daniel Rudolf:
Tractability of the approximation of high-dimensional rank one tensors
submitted manuscript, 02/2014,
Constructive Approximation 43 (2016), 1--13.
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96) With Mario Ullrich and Henryk Wozniakowski:
Complexity of oscillatory integration for univariate Sobolev spaces,
submitted manuscript, 11/2013
J. Complexity 31 (2015), 15-41.
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95) With Daniel Rudolf:
Computation of expectations by Markov chain Monte Carlo methods,
submitted manuscript, 11/2013
In: "Extraction of quantifiable information from complex systems", S. Dahlke et al. (eds.), Springer, 2014.
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94) With Aicke Hinrichs and Mario Ullrich:
On weak tractability of the Clenshaw-Curtis Smolyak algorithm,
submitted manuscript, 09/2013. J. Approximation Th. 183, 31-44, 2014.
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93) With Aicke Hinrichs, Mario Ullrich and Henryk Wozniakowski:
The curse of dimensionality for numerical integration of smooth functions II,
submitted manuscript, 04/2013, goto arxiv
J. Complexity 30 (2014), 117-143.
92) With Aicke Hinrichs, Mario Ullrich and Henryk Wozniakowski:
The curse of dimensionality for numerical integration of smooth functions, 11/2012,
Math. Comp. Vol. 83, 2014, 2853-2863.
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91) With H. Wozniakowski:
Tractability of Multivariate Problems, Volume III: Standard Information for Operators
EMS Tracts in Mathematics, Vol. 18
Eur. Math. Soc. Publ. House , Zürich 2012
info
90) With Th. Müller-Gronbach and K. Ritter:
Monte Carlo-Algorithmen
Springer Verlag, Berlin, 2012
To info of the publisher.
Hier eine Liste von Fehlern und Hinweisen.
89) With A. Hinrichs and H. Wozniakowski:
Discontinuous information in the worst case and randomized settings
May 2011, September 2011. Mathematische Nachrichten 286, 679-690, 2013. pdf-file
88) With A. Hinrichs and H. Wozniakowski:
The curse of dimensionality for the class of monotone functions and for the class of convex functions
September 2010, December 2010. J. Approx. Th. 163 (2011), 955-965.
pdf-file
87) With H. Wozniakowski:
On the power of function values for the approximation problem in various settings
September 2010, June 2011 (final version),
Surveys in Approximation Theory 6 (2011), 1-23.
pdf-file
86) With H. Wozniakowski:
Lower bounds for the complexity of linear functionals in the randomized setting
J. Complexity 27 (2011), 1-22.
pdf-file
85) With H. Wozniakowski:
Tractability of Multivariate Problems, Volume II: Standard Information for Functionals
EMS Tracts in Mathematics, Vol. 12
Eur. Math. Soc. Publ. House , Zürich 2010
info
84) With H. Wozniakowski:
Tractability of approximating multivariate linear functionals.
In: The Steve Smale Festschrift.
J. Fixed Point Th. Appl. 7 (2010), 313-324.
pdf-file
With I. H. Sloan, J. F. Traub and H. Wozniakowski:
Essays on the Complexity of Continuous Problems,
Eur. Math. Soc., Zürich 2009.
Info of the publisher.
83) With S. Dahlke and W. Sickel:
Optimal approximation of elliptic problems by linear and nonlinear mappings IV: errors in L_2 and other norms.
June 2009. J. Complexity 26 (2010), 102-124.
ps-file, pdf-file
82) With H. Wozniakowski:
Approximation of infinitely differentiable multivariate functions is intractable
September 2008
Journal of Complexity 25 (2009), 398-404.
pdf-file
81) Henryk Wozniakowski and the complexity of continuous problems
August 2008
pdf-file
80) With H. Wozniakowski:
Tractability of Multivariate Problems, Volume I: Linear Information
EMS Tracts in Mathematics, Vol. 6
Eur. Math. Soc. Publ. House, Zürich 2008
pdf-file for a flyer.
pdf-file for the whole book.
79) With H. Wozniakowski:
Optimal order of convergence and (in)tractability of multivariate approximation of smooth functions
July 2008, Constructive Approximation 30 (2009), 457-473.
pdf-file
78) With A. Hinrichs and J. Vybiral:
Linear information versus function evaluations for L_2-approximation
December 2007.
Journal Approximation Theory 153 (2008), 97-107.
ps-file, pdf-file
77) With H. Wozniakowski:
L_2 Discrepancy and Multivariate Integration.
November 2007.
In: Analytic Number Theory: Essays in Honour of Klaus Roth.
Cambridge University Press, pp. 359-388, 2009.
ps-file, pdf-file
76) Was können Quantencomputer?
Dezember 2006.
Mathematische Semesterberichte 54 (2007), 31-38. Springer Verlag.
ps-file, pdf-file
75) With P. Mathe:
Simple Monte Carlo and the Metropolis algorithm.
November 2006, April 2007.
J. Complexity 23 (2007), 673-696.
ps-file, pdf-file
74) With S. Dahlke and W. Sickel:
Optimal approximation of elliptic problems by linear and nonlinear mappings III: frames.
November 2006, March 2007.
J. Complexity 23 (2007), 614-648.
ps-file, pdf-file
73) With A. Hinrichs:
Cubature Formulas for Symmetric Measures in Higher Dimensions with Few Points.
August 2005, February 2006.
Math. of Comp. 76 (2007), 1357-1372.
ps-file, pdf-file
72) With S. Dahlke and W. Sickel:
Optimal approximation of elliptic problems by linear and nonlinear mappings II.
September 2005, March 2006.
J. Complexity 22 (2006), 549-603. ps-file, pdf-file
71) With S. Dahlke and W. Sickel:
Optimal approximation of elliptic problems by linear and nonlinear mappings I.
Oct. 2004, May 2005.
J. Complexity 22 (2006), 29-49.
ps-file, pdf-file
70) With H. Triebel:
Function spaces in Lipschitz domains and optimal rates of convergence for sampling.
May 2004, Preprint.
ps-file, pdf-file
A slightly shorter version: Constr. Approx. 23 (2006), 325-350.
69) With H. Pfeiffer:
Coin tossing algorithms for integral equations and tractability.
Monte Carlo Methods and Appl. 10 (2004), 491-498.
ps-file
68) With S. Heinrich and H. Pfeiffer:
How many random bits do we need for Monte Carlo integration?
In: Monte Carlo and Quasi-Monte Carlo Methods 2002. H. Niederreiter (ed.). Springer 2004, p. 27-49.
ps-file
67) With I. H. Sloan and H. Wozniakowski:
Tractability of Approximation for Weighted Korobov Spaces on Classical and Quantum Computers.
Found. Comput. Math. 4 (2004), 121--156.
abstract and paper
Gleichmässige Verteilung von Punkten in einem Würfel.
Die Wurzel, 2004, 239-246.
ps-file
66) With S. Heinrich: On a Problem in Quantum Summation.
J. Complexity 19 (2003), 1-18.
abstract and paper
65) With S. Heinrich:
Optimal Summation and Integration by Deterministic, Randomized, and Quantum Algorithms.
In: Monte Carlo and Quasi-Monte Carlo Methods 2000, K.-T. Fang, F. J. Hickernell, H. Niederreiter (Eds.)
pp. 50-62, Springer Verlag, 2002.
abstract and paper
64) Quantum Complexity of Integration
J. Complexity 17 (2001), 2-16.
abstract and paper
63) With R. Cools:
Spherical product algorithms and the integration of smooth
functions with one singular point.
Preprint, July 2000. SIAM J. Numer. Anal. 39 (2001), 1132-1145.
abstract and paper
62) With H. Wozniakowski:
IBC-Problems Related to Steve Smale.
In: Foundatations of Computational Mathematics. Proceedings of the Smalefest 2000.
F. Cucker, J. M. Rojas (eds.), World Scientific 2002, pp. 295-318. ps-file
61) With H. Wozniakowski:
When are integration and discrepancy tractable?
In: Foundations of Computational Mathematics. R. A. DeVore, A. Iserles, E. Süli (eds),
Cambridge University Press, 2001, 211-266.
abstract, ps-file
60) With S. Heinrich, G. W. Wasilkowski, H. Wozniakowski:
The inverse of the star-discrepancy depends linearly on the dimension.
Acta Arithmetica 96 (2001), 279-302.
abstract, ps-file
59) With H. Wozniakowski:
Intractability results for integration and discrepancy.
J. Complexity 17 (2001), 388-441.
abstract, ps-file
58) Numerische Verfahren für Hochdimensionale Probleme und der Fluch der Dimension.
Jahresbericht der DMV 101 (1999), 151-177.
abstract, ps-file
57) Is there a curse of dimension for integration?
Eleventh Int. Conf. on Domain Decomposition Methods.
C.-H. Lai, P. E. Bjorstad, M. Cross, O. B. Widlund, eds., 1999, 88-95. Published by Domain Decomposition Press, Bergen.
abstract, ps-file
56) With V. Barthelmann and K. Ritter:
High dimensional polynomial interpolation on sparse grids.
Advances in Computational Mathematics 12 (1999), 273-288.
abstract, ps-file
55) Intractability results for positive quadrature formulas
and extremal problems for trigonometric polynomials.
J. Complexity 15 (1999), 299-316.
abstract, ps-file
54) With K. Ritter and A. Steinbauer:
A multiscale method for the evaluation of Wiener integrals.
Approximation Theory IX, Volume 2: Computational Aspects.
C. K. Chui, L. L. Schumaker (eds.), 251-258, 1998.
abstract, ps-file
53) With Henryk Wozniakowski:
Complexity of linear problems with a fixed output basis.
Journal of Complexity 16 (2000), 333-362.
abstract, ps-file
52) With R. Cools and K. Ritter:
Smolyak's construction of cubature formulas of arbitrary trigonometric degree.
Computing 62 (1999), 147-162.
abstract, ps-file
51) With H. Wozniakowski:
On the cost of uniform and nonuniform algorithms.
Th. Comp. Sci. 219 (1999), 301-318.
abstract, ps-file
50) With K. Ritter:
Simple cubature formulas with high polynomial exactness.
Constructive Approximation 15 (1999), 499-522.
abstract, ps-file
49) With K. Ritter, R. Schmitt and A. Steinbauer:
On an interpolatory method for high dimensional integration.
J. Comput. Appl. Math. 112 (1999), 215-228.
abstract, ps-file
48) With I. H. Sloan and H. Wozniakowski:
Tractability of tensor product linear operators.
J. Complexity 13 (1997), 387-418.
abstract, pdf-file
47) With K. Ritter:
The curse of dimension and a universal method
for numerical integration.
In: Multivariate Approximation and Splines,
G. Nürnberger, J. W. Schmidt, G. Walz (eds.), ISNM, 1997, 177-188.
abstract, ps-file
46) High dimensional numerical problems.
Nonlinear Analysis, Vol. 30 (1996), 1439-1446.
45) With I. Roschmann:
Numerical integration of peak functions.
J. Complexity 12 (1996), 358-379.
abstract, ps-file
44) With H. Wozniakowski:
Topological complexity of zero finding.
J. Complexity 12 (1996), 380-400.
abstract, ps-file
43) On the power of adaption.
J. Complexity 12 (1996), 199-237.
abstract, ps-file
42) Error bounds for adaptive methods.
ZAMM, Special issues for the ICIAM/GAMM conference,
Hamburg, July 3-7, 1995, Issue 3, 113-115.
41) The Bayesian approach to numerical problems: results for zero finding.
Proc. of the IMACS-GAMM Int. Symp. on Numerical Methods and Error Bounds.
Akademie Verlag, Berlin, 1996, 164-171.
ps-file
40) With C. Katscher and K. Petras:
Quadrature formulas for multivariate convex functions.
ps-file J. Complexity 12 (1996), 5-16.
39) With Klaus Ritter:
High dimensional integration of smooth functions over cubes.
Numer. Math. 75 (1996), 79-97.
abstract, ps-file
38) With Klaus Ritter:
Global optimization using hyperbolic cross points
In: State of the Art in Global Optimization (C. A. Floudas, P. M. Pardalos, eds.),
pp. 19-33, Kluwer, Dordrecht, 1996.
abstract , ps-file
37) With K. Ritter and H. Wozniakowski:
Average case optimality of a hybrid secant-bisection method
Math. Comp. 64 (1995), 1517-1539. ps-file
36) The adaption problem for nonsymmetric convex sets.
J. Approx. Theory 82 (1995), 123-134.
35) The real number model in numerical analysis.
J. Complexity 11 (1995), 57-73.
abstract, ps-file
34) Optimal recovery and n-widths for convex classes of functions.
J. Approx. Theory 80 (1995), 390-408.
33) With K. Petras:
Optimal stochastic quadrature formulas for convex functions.
BIT 34 (1994), 288-294.
32) With K. Ritter:
Some complexity results for zero finding for univariate functions.
J. Complexity 9 (1993), 15-40. ps-file
31) Quadrature formulas for convex classes of functions.
In: Numerical Integration IV, H. Brass and G. Hämmerlin (eds.),
ISNM 112, 283-296. Birkhäuser, 1993.
30) Effective numerical methods and average errors.
In: Operations Research '92, Physica-Verlag, 207-210, Heidelberg, 1993
29) Algorithms and complexity for continuous problems.
In `Geometry, Analysis, and Mechanics', J. M. Rassias, ed., World Scientific,
Singapore, 1994, pp. 157-188.
28) With H. Wozniakowski:
Relaxed verification for continuous problems.
J. Complexity 8 (1992), 124-152.
27) With H. Eydam, H. Novak, K. Probst, K. Ritter and O. Szüszner:
Überwachung des Oberbeckens des Pumpspeicherwerkes Happurg.
Wasserwirtschaft 91 (1991), 505-517.
26) With K. Ritter:
Average errors for zero finding: lower bounds.
Math. Zeitschrift 211 (1992), 671-686.
25) Optimal linear randomized methods for linear operators in Hilbert spaces.
J. of Complexity 8 (1992), 22-36.
24) Some applications of functional integration: average errors of numerical methods.
Suppl. Rend. Circ. Mat. Palermo. 28 (1992), 425-437.
23) Quadrature formulas for monotone functions.
Proc. of the AMS. 115 (1992), 59-68. ps-file
22) With M. Kon: The adaption problem for approximating linear operators.
Bulletin of the AMS 23 (1990), 159-165.
21) Stochastic error bounds for some nonlinear problems in numerical analysis.
In: Approximation Theory VI, Vol. 2, C. K. Chui, L. L. Schumaker and J. D. Ward (eds.),
pp. 503-506, Academic Press, 1989.
20) Average case results for zero finding.
J. Complexity 5 (1989), 489-501.
19) Determining zeroes of increasing Lipschitz functions.
Aequationes Math. 41 (1991), 161-167.
18) With M. Kon:
On the adaptive and continuous information problems.
J. Complexity 5 (1989), 345-362.
17) With S. Graf and A. Papageorgiou:
Bisection is not optimal on the average.
Numer. Math. 55 (1989), 481-491.
16) Stochastic properties of quadrature formulas.
Numer. Math. 53 (1988), 609-620.
15) With K. Ritter:
A stochastic analog to Chebyshev centers and optimal average case algorithms.
J. Complexity 5 (1989), 60-79.
14) With S. Graf:
The average error of quadrature formulas for functions of bounded variation.
Rocky Mountain J. Math. 20 (1990), 707-716.
13) Deterministic and stochastic error bounds in numerical analysis.
Lecture Notes in Mathematics 1349, Springer-Verlag, 1988. 113 pages.
This book was out of print, but is available again.
12) A decomposition of measures in euclidean space
yielding error bounds for quadrature formulas.
Math. Z. 196 (1987), 407-413.
11) On the convergence of interpolated iteration methods.
SIAM J. Math. Anal. 19 (1988), 1174-1182.
10) With H. Grabmüller:
Nonlinear boundary value problems for the annular membrane:
New results on existence of positive solutions.
Math. Methods Appl. Sci. 10 (1988), 37-49.
9) With H. Grabmüller:
Nonlinear boundary value problems for the annular membrane:
A note on uniqueness of positive solutions.
Journal Elasticity 17 (1987), 279-284.
8) The average a posteriori error of numerical methods.
Numer. Math. 50 (1986), 245-252.
7) On average case errors in numerical analysis.
J. Complexity 2 (1986), 229-238.
6) An elementary approach to unsmoothing over cubes.
Indag. Math. 48 (1986), 209-212.
5) With I. K. Rana:
On the unsmoothing of functions on the real line.
Indag. Math. 48 (1986), 201-207.
4) Two remarks on the decreasing rearrangement of a function.
J. Math. Anal. Appl. 122 (1987), 485-486.
3) Quadrature and widths.
J. Approx. Theory 47 (1986), 195-202.
2) Eingeschränkte Monte Carlo-Verfahren zur numerischen Integration.
Proc. 4th Pannonian Symp. on Math. Statist., Bad Tatzmannsdorf, Austria 1983.
W. Grossmann et al. eds. Reidel, 1985, pp. 269-282.
1) Einige ergänzende Bemerkungen zur eps-Entropie und eps-Kapazität im R^n.
Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, 191 (1982), 1-8.
0) Zur unteren Fehlergrenze von Quadraturverfahren.
Dissertation, Erlangen 1983, 94 pages.