Product rules are optimal for numerical integration in classical smoothness spaces

N. S. Bakhvalov, On the approximate calculation of multiple integrals, J. Complexity 31

1959

Earlier work this paper cites.

S. A. Smolyak, On optimal restoration of functions and functionals of them (in Russian), Candidate Dissertation, Moscow State University, 1965

1965

Earlier work this paper cites.

S. Haber, Numerical evaluation of multiple integrals, SIAM Reviews 12

1970

Earlier work this paper cites.

N. S. Bakhvalov, On the optimality of linear methods for operator approximation in convex classes of functions (in Russian), Zh. Vychisl, Mat. Mat. Fiz. 11

1971

Earlier work this paper cites.

V. P. Motornyĭ, The best quadrature formula of the form ∑ k = 1 n p k ​ f ​ ( x k ) \sum_{k=1}^{n}p_{k}f(x_{k}) for certain classes of periodic differentiable functions (in Russian), Dokl. Akad. Nauk SSSR , 221, 1060–1062, 1973, [English transl.: Soviet Math. Dokl., 14, 1180–1183, 1973]

1973

Earlier work this paper cites.

V. P. Motornyĭ, The best quadrature formula of the form ∑ k = 1 n p k ​ f ​ ( x k ) \sum_{k=1}^{n}p_{k}f(x_{k}) for certain classes of periodic differentiable functions (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. , 38, 583–614, 1974, [English transl.: Math. USSR-Izv., 8, 591–620, 1974]

1974

Cited alongside, same era.

A. G. Sukharev, Optimal numerical integration formulas for some classes of functions of several variables, Soviet Math. Dokl. 20

1979

Cited alongside, same era.

G. W. Wasilkowski, Some nonlinear problems are as easy as the approximation problem, Comput. Math. Appl. 10

1984

Cited alongside, same era.

E. Novak, Deterministic and Stochastic Error Bounds in Numerical Analysis , LNiM 1349

1988

Cited alongside, same era.

J. F. Traub, G. W. Wasilkowski and H. Woźniakowski, Information-Based Complexity , Academic Press, 1988

1988

P. Köhler, Intermediate error estimates for quadrature formulas, in: Numerical integration, IV (Oberwolfach, 1992), Internat. Ser. Numer. Math. 112

1993

Later among the works it cites.

K. Petras, Gaussian quadrature formulae, second Peano kernels, nodes, weights and Bessel functions, Calcolo 30

1993

Later among the works it cites.

E. Novak and H. Woźniakowski, Tractability of Multivariate Problems , Volume I: Linear Information, European Math. Soc. Publ. House, Zürich, 2008

2008

Later among the works it cites.

E. Novak and H. Woźniakowski, Tractability of Multivariate Problems , Volume II: Standard Information for Functionals, European Math. Soc. Publ. House, Zürich, 2010

2010

Later among the works it cites.

A. Hinrichs, E. Novak, M. Ullrich, H. Woźniakowski, The curse of dimensionality for numerical integration of smooth functions, Math. Comp. 83

2014