Results 201 to 210 of about 1,730 (224)
Some of the next articles are maybe not open access.
Optimal stochastic quadrature formulas for convex functions
BIT, 1994Optimal stochastic (Monte Carlo) quadrature formulas for defined classes of convex functions are studied. Specifically, non-adaptive Monte Carlo methods are seen to be no better than deterministic methods, but adaptive Monte Carlo methods are shown to exhibit a superior performance.
Novak, E., Petras, K.
openaire +2 more sources
Asymptotic Properties of Optimal Quadrature Formulas
1979In [9], Sard introduced a notion of “best” for quadrature formulas which may be described as follows. Let 0 = t0 < t1 < ... < tN = 1 be fixed points, and consider the formula $${Q_N}(f) \equiv \sum\limits_{i = 0}^N {{c_i}f({t_i}) \simeq \int_0^1 f (\tau )} d\tau \equiv I(f)$$ (1) .
David L. Barrow, Philip W. Smith
openaire +1 more source
THE EXISTENCE OF OPTIMAL QUADRATURE FORMULAS WITH GIVEN MULTIPLICITIES OF NODES
Mathematics of the USSR-Sbornik, 1978Suppose that is the error of the best method of integration in the class with nodes of multiplicities , i.e. . It is then shown that for and for every system of multiplicities with for , the lower bound is attained for some nodes with exactly the multiplicities . Moreover, and .Bibliography: 20 titles.
openaire +2 more sources
ON BEST AND OPTIMAL QUADRATURE FORMULAS ON CLASSES OF BOUNDED ANALYTIC FUNCTIONS
Mathematics of the USSR-Izvestiya, 1989See the review in Zbl 0647.30033.
openaire +2 more sources
A Class of Optimal Quadrature Formulae
IMA Journal of Numerical Analysis, 1983Raina, B. L., Kaul, N.
openaire +2 more sources
Optimal Quadrature Formulae for Periodic Functions
1974We consider \( {\tilde H_\beta }: = \left\{ {f\left| {2\pi - } \right.} \right. \) periodic, holomorphic in a strip of width 2β, real on ℝ with \( {\left| f \right|_\beta }: = \mathop {\sup }\limits_{\left| y \right| < \beta } \left| {\operatorname{Re} f\left( {x + iy} \right)} \right| < \infty \} \) and \( \tilde H_\beta ^1 = \left\{ {f \in {{\tilde H}
openaire +1 more source
On the existence of optimal quadrature formulae for smooth functions
Calcolo, 1979A general method showing the existence of optimal quadrature formulae with preassigned multiplicities of the nodes for classes of smooth functions is demonstrated. The main result is applied to the Hardy spaceH ∞ of analytic functions.
openaire +2 more sources
Widths and optimal quadrature formulas for convolution classes
Ukrainian Mathematical Journal, 1991We compute Kolmogorov widths in the space L1 for classes of periodic functions representable in the form of a kernel convolution that does not increase the number of sign changes with values in a given transposition invariant set of functions, and solve the optimization problem for quadrature formulas in these classes.
openaire +1 more source
An optimal quadrature formula of closed type
Yokohama mathematical journal, 2003An optimal 3-point quadrature formula of closed type is derived. The optimality is considered with respect to a given way of estimation of its error.
openaire +2 more sources
Construction of an Optimal Quadrature Formula in the Hilbert Space of Periodic Functions
Lobachevskii Journal of Mathematics, 2023exaly