Zobrazeno 1 - 10
of 68
pro vyhledávání: '"Borislav Bojanov"'
Autor:
Borislav Bojanov
Publikováno v:
Rendiconti di Matematica e delle Sue Applicazioni, Vol 25, Iss 2, Pp 195-221 (2005)
We discuss quadrature formulae of highest algebraic degree of precision for integration of functions of one or many variables which are based on non-standard data, i.e., in which the information used is different from the standard sampling of functio
Externí odkaz:
https://doaj.org/article/cd1d9b86fcce43d4bdb8ad544b695c03
Autor:
Guergana Petrova, Borislav Bojanov
Publikováno v:
Journal of Approximation Theory. 162(10):1788-1792
We give a bivariate analog of the Micchelli–Rivlin quadrature for computing the integral of a function over the unit disk using its Radon projections.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7c4e31d3b393c607b020c4dec7adfb7b
Autor:
Yuan Xu, Borislav Bojanov
Publikováno v:
SIAM Journal on Mathematical Analysis. 37:238-250
A polynomial of degree $n$ in two variables is shown to be uniquely determined by its Radon projections taken over $[n/2]+1$ parallel lines in each of the $(2[(n+1)/2]+1)$ equidistant directions along the unit circle.
SIAM J. Math. Anal. (to app
SIAM J. Math. Anal. (to app
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::062d4c4b4e3bc61a4bb99a21eff4b6aa
https://doi.org/10.1137/040616516
https://doi.org/10.1137/040616516
Autor:
Petar Petrov, Borislav Bojanov
Publikováno v:
SIAM Journal on Numerical Analysis. 43:787-795
For any given system of continuously differentiable functions $\{u_k\}_{k=1}^{2n}$ that constitute an extended Tchebycheff system of order 2 on [a,b] we prove the existence and uniqueness of the Gaussian interval quadrature formula based on n weighte
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::65aced682fcfdd71369d08ecf31de17b
https://doi.org/10.1137/040606521
https://doi.org/10.1137/040606521
Autor:
Borislav Bojanov
Publikováno v:
Indagationes Mathematicae. 15:469-483
We prove that for every χ[−1, 1] and every real algebraic polynomial f of degree n such that | f ( t ): ⩽ 1 on [−1, 1], the following inequality takes place on the complex plane | f ( x + i y ) | ⩽ | T n ( 1 + i y ) | , − ∞ ⩽ y ⩽ ∞
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::014301aaa8d601667b15b10611f906f1
https://doi.org/10.1016/s0019-3577(05)00002-9
https://doi.org/10.1016/s0019-3577(05)00002-9
Autor:
Petar Petrov, Borislav Bojanov
Publikováno v:
Numerische Mathematik. 95:53-62
We prove that for a given finite interval [a, b] and any set of preassigned non-negative numbers h 1 ,?,h n such that h 1 +a?+h n
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8382161b6eb4af18d5db40f55c005fff
https://doi.org/10.1007/s00211-002-0433-x
https://doi.org/10.1007/s00211-002-0433-x
Autor:
Yuan Xu, Borislav Bojanov
Publikováno v:
Journal of Approximation Theory. 120(2):267-282
Polynomial interpolation of two variables based on points that are located on multiple circles is studied. First, the poisedness of a Birkhoff interpolation on points that are located on several concentric circles is established. Second, using a fact
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e99c25df742123bdd27602236f7e9ace
Autor:
Yuan Xu, Borislav Bojanov
Publikováno v:
SIAM Journal on Numerical Analysis. 39:1780-1793
A problem of Hermite interpolation by polynomials of two variables is studied. The interpolation matches preassigned data of function values and consecutive normal derivatives on a set of points on several circles centered at the origin. It includes
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::77e23fccdaf0f65fb2324d12fa5bfdea
https://doi.org/10.1137/s0036142901383478
https://doi.org/10.1137/s0036142901383478
Publikováno v:
Canadian Journal of Mathematics. 53:489-505
Bivariate polynomials with a fixed leading term xmyn, which deviate least fromzero in the uniform or L2-norm on the unit disk D (resp. a triangle) are given explicitly. A similar problem in Lp, 1 ≤ p ≤ ∞, is studied on D in the set of products
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c1c4c433fc35bfb30db07c17be0faee3
https://doi.org/10.4153/cjm-2001-021-3
https://doi.org/10.4153/cjm-2001-021-3
Autor:
Petar P. Petrov, Borislav Bojanov
Publikováno v:
Numerische Mathematik. 87:625-643
We prove the existence of a Gaussian quadrature formula for Tchebycheff systems, based on integrals over non-overlapping subintervals of arbitrary fixed lengths and the uniqueness of this formula in the case the subintervals have equal lengths.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::35ee451471c2c3c9165282bb95b7d22f
https://doi.org/10.1007/pl00005426
https://doi.org/10.1007/pl00005426