Results 1 to 10 of about 2,749,932 (104)

Weighted Optimal Quadrature Formulas in Sobolev Space and Their Applications

Algorithms
Optimization of computational algorithms is one of the main problems of computational mathematics. This optimization is well demonstrated by the example of the theory of quadrature and cubature formulas. It is known that numerical integration of definite integrals is of great importance in basic and applied sciences.
Kholmat Shadimetov
exaly   +4 more sources

On an Optimal Quadrature Formula in a Hilbert Space of Periodic Functions

Algorithms, 2022
The present work is devoted to the construction of optimal quadrature formulas for the approximate calculation of the integrals ∫02πeiωxφ(x)dx in the Sobolev space H˜2m. Here, H˜2m is the Hilbert space of periodic and complex-valued functions whose m-th generalized derivatives are square-integrable.
Abdullo Hayotov
exaly   +4 more sources

Uniqueness of the Optimal Nodes of Quadrature Formulae [PDF]

Mathematics of Computation, 1981
We prove the uniqueness of the quadrature formula with minimal error in the space W
openaire   +2 more sources

Comparison of optimal quadrature formulas

Numerische Mathematik, 1989
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bojanov, Borislav, Huang, Daren
openaire   +1 more source

Error Bounds for Optimal Definite Quadrature Formulae

Journal of Approximation Theory, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kohler, P., Nikolov, G.
openaire   +1 more source

On optimal quadrature formulae

Journal of Inequalities and Applications, 2000
For integrals involving a nonnegative weight function on a finite interval the author proposes a procedure to construct quadrature formulas which are exact for solutions of linear differential equations and are optimal in the sense of Sard. The author establishes necessary and sufficient conditions for the existence of such formulas.
openaire   +3 more sources

Asymptotically optimal definite quadrature formulae of 4th order

Journal of Computational and Applied Mathematics, 2017
26 pages, 4 figures, 4 ...
Ana Avdzhieva, Geno P. Nikolov
openaire   +3 more sources

On certain optimal quadrature formulas

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences, 1971
IS any Npoint quadrature formula, and E(l(f) =/(f) -Q(f) where /(f) is the integral which Q is approximating, we shall denote by "cr(EQ)" the "RMS" average of Ell with respect to Sarma's measure. Sarma calls a formula Q.I' "completely optimal" if cr(EC1s) :s; cr(ECl ~\,) for every N·point formula Q~; and he calls it "optimal in the weights" if cr(EClN )
openaire   +2 more sources

Optimization of the Approximate Integration Formula Using the Quadrature Formula

International Journal of Analysis and Applications
The article explores Sard’s problem of constructing optimal quadrature formulas in the space W(4,0)2(0,1) by using Sobolev’s method. This problem involves two steps: first, calculating the norm of the error functional, and then finding the minimum of this norm by the coefficients of the quadrature formulas.
Kh.M. Shadimetov, A.K. Boltaev
openaire   +1 more source

Optimal quadrature formulae on the real line

Journal of Mathematical Analysis and Applications, 1992
Quadrature formulas with equidistant nodes on the real line, involving a sequence of derivatives are treated. In this class, an optimal quadrature formula is obtained for the Sobolev space of functions with an additional restriction on its Fourier transforms. An explicit expression for the error is given.
openaire   +2 more sources