Constructive sparse trigonometric approximation and other problems for functions with mixed smoothness

S. B. Stechkin, On the best approximation of given classes of functions by arbitrary polynomials,Uspekhi Mat. Nauk 9

1954

Earlier work this paper cites.

R.S. Ismagilov, Widths of sets in normed linear spaces and the approximation of functions by trigonometric polynomials, Uspekhi Mat. Nauk, 29

1974

Earlier work this paper cites.

Y. Makovoz, On trigonometric n n -widths and their generalizations, J. Approx. Theory 41

1984

Earlier work this paper cites.

V.E. Maiorov, Trigonometric diameters of the Sobolev classes W p r W^{r}_{p} in the space L q L_{q} , Math. Notes 40

1986

Earlier work this paper cites.

V.N. Temlyakov, Approximation of Periodic Functions of Several Variables by Bilinear Forms, Izvestiya AN SSSR, 50

1987

Earlier work this paper cites.

V.N. Temlyakov, Approximate recovery of periodic functions of several variables, Mat. Sb., 128

1987

Earlier work this paper cites.

E. S. Belinskii, Approximation by a ”floating” system of exponentials on classes of smooth periodic functions, Matem. Sb. 132

1988

Earlier work this paper cites.

E.D. Gluskin, Extremal properties of orthogonal parallelpipeds and their application to the geometry of Banach spaces, Math USSR Sbornik 64

1989

Earlier work this paper cites.

V.N. Temlyakov, Approximation of functions with bounded mixed derivative, Trudy MIAN, 178

1989

Earlier work this paper cites.

V.N. Temlyakov, Estimates of the asymptotic characteristics of classes of functions with bounded mixed derivative or difference, Trudy Matem. Inst. Steklov

1990

Earlier work this paper cites.

V.N. Temlyakov, On a way of obtaining lower estimates for the errors of quadrature formulas, Matem. Sbornik, 181

1992

Cited alongside, same era.

V.N. Temlyakov, On Approximate Recovery of Functions with Bounded Mixed Derivative, J. Complexity, 9

1993

Cited alongside, same era.

V.N. Temlyakov, Approximation of periodic functions

1993

Cited alongside, same era.

B.S. Kashin and V.N. Temlyakov, On best m m -term approximations and the entropy of sets in the space L 1 L^{1} , Math. Notes

1994

Cited alongside, same era.

R.A. DeVore and V.N. Temlyakov, Nonlinear approximation by trigonometric sums, J. Fourier Analysis and Applications, 2

1995

Cited alongside, same era.

V.N. Temlyakov, An inequality for trigonometric polynomials and its application for estimating the entropy numbers, J. Complexity

V.N. Temlyakov, Weak greedy algorithms, Advances in Comput. Math. 12

2000

Later among the works it cites.

V.N. Temlyakov, Greedy algorithms in Banach spaces, Advances in Comput. Math. 14

2001

Later among the works it cites.

S.J. Dilworth, D. Kutzarova, V.N. Temlyakov, Convergence of some Greedy Algorithms in Banach spaces, The J. Fourier Analysis and Applications 8

2002

Later among the works it cites.

A.S. Romanyuk, Best M M -term trigonometric approximations of Besov classes of periodic functions of several variables, Izvestia RAN, Ser. Mat. 67

2003

Later among the works it cites.

V.N. Temlyakov, Cubature formulas and related questions, J. Complexity 19

2003

Later among the works it cites.

V.N. Temlyakov, Greedy-Type Approximation in Banach Spaces and Applications, Constr. Approx. 21