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- Borislav Bojanov, Petar Peynov Petrov
- Numerische Mathematik
- 2001

- Borislav Bojanov, Guergana Petrova
- 2003

We derive in a simple way certain minimal cubature formulae, obtained by Morrow and Patterson [2], and Xu [4], using a different technique. We also obtain in explicit form new near minimal cubature formulae. Then, as a corollary, we get a compact expression for the bivariate Lagrange interpolation polynomials, based on the nodes of the cubature.

- Borislav Bojanov
- 1999

Let p n be a polynomial of m variables and total degree n such that & p n & C(K) =1, where K/R m is a convex body. In this paper we discuss some local and uniform estimates for the magnitude of grad p n under the above conditions. 1999 Academic Press Key Words: multivariate polynomials; convex bodies; gradient and directional derivative of polynomials.

- Borislav Bojanov, Yuan Xu
- Journal of Approximation Theory
- 2003

- Borislav Bojanov, Guergana Petrova
- Numerische Mathematik
- 1998

The ordinary type of information data for approximation of functions f or functionals of them in the univariate case consists of function values {f(x1), . . . , f(xm)}. The classical Lagrange interpolation formula and the Gauss quadrature formula are famous examples. The simplicity of the approximation rules, their universality, the elegancy of the proofs… (More)

- Borislav Bojanov, Dimitar K. Dimitrov
- Math. Comput.
- 2001

The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula… (More)

- Borislav Bojanov, Petar Peynov Petrov
- Numerische Mathematik
- 2003

- Borislav Bojanov, Yuan Xu
- SIAM J. Numerical Analysis
- 2002

This is the story of the classical Markov inequality for the k-th derivative of an algebraic polynomial, and of the remarkably many attempts to provide it with alternative proofs that occurred all through the last century. In our survey we inspect each of the existing proofs and describe, sometimes briefly, sometimes not very briefly, the methods and ideas… (More)

- Borislav Bojanov, Guergana Petrova
- 2008

We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Michhelli and Sharma and construct new Gaussian formulas… (More)