Kh. M. Shadimetov, N. H. Mamatova, “Compound cubature formulas on a lattice”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, Number 11,Pages <nobr>59

Compound cubature formulas on a lattice

Kh. M. Shadimetov^ab, N. H. Mamatova^cb

^a Tashkent State Transport University, 1 Odilkhodjaev str., Tashkent, 100167 Republic of Uzbekistan
^b V.I. Romanovskiy Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, 81 Mirzo Ulugbek str., Tashkent, 100174 Republic of Uzbekistan
^c Bukhara State University, 11 M. Iqbol str., Bukhara, 200118 Republic of Uzbekistan

Abstract: In the present paper lattice optimal cubature formulas are constructed by the variational method in the Sobolev space. In addition, the square of the norm of the error functional of the constructed lattice optimal cubature formulas in the conjugate Sobolev space is explicitly calculated.

Keywords: Sobolev space, extremal function, composite lattice optimal cubature formulas, error functional.

UDC: 519.644

Received: 29.03.2023
Revised: 29.03.2023
Accepted: 29.05.2023

DOI: 10.26907/0021-3446-2023-11-59-74