2006 , Volume 11, Special issue, p.19-26

In the paper we examine how the error of a given cubature formula varies under small perturbations of its weights. Considering this problem in Sobolev spaces of periodic functions of finite smoothness we establish that the norm of a perturbed error functional does not exceed one and a half of the norm of the initial error functional provided that the number of nodes of a cubature formula under study is not greater then some upper boundary. This upper boundary depends on the smoothness of integrands, the dimension of the space of independent variables, and the constants of the machine arithmetic.