Lower bound for the Lebesgue function of an interpolation process with algebraic polynomials on equidistant nodes of a simplex

2012 ◽  
Vol 92 (1-2) ◽  
pp. 16-22
Author(s):  
N. V. Baidakova
Keyword(s):  
Lower Bound ◽  
Interpolation Process ◽  
Lebesgue Function ◽  
Algebraic Polynomials ◽  
Equidistant Nodes

scholarly journals On the Lebesgue function for lagrange interpolation with equidistant nodes

1992 ◽  
Vol 52 (1) ◽  
pp. 111-118 ◽  
Author(s):  
T. M. Mills ◽  
Simon J. Smith
Keyword(s):  
Asymptotic Expansion ◽  
Lower Bounds ◽  
Lagrange Interpolation ◽  
Upper And Lower Bounds ◽  
Lebesgue Function ◽  
Equidistant Nodes ◽  
Image Position

AbstractProperties of the Lebesgue function associated with interpolation at the equidistant nodes , are investigated. In particular, it is proved that the relative maxima of the Lebesgue function are strictly decreasing from the outside towards the middle of the interval [0, n], and upper and lower bounds, and an asymptotic expansion, are obtained for the smallest maximum when n is odd.

scholarly journals On Hermite-Fejér interpolation with equidistant nodes

1990 ◽  
Vol 48 (3) ◽  
pp. 461-471
Author(s):  
G. B. Baker ◽  
T. M. Mills ◽  
P. Vértesi
Keyword(s):  
Interpolation Process ◽  
Infinite Interval ◽  
Approximation Properties ◽  
Interpolation Of Functions ◽  
Equidistant Nodes

AbstractThis paper deals with Hermite-Fejér interpolation of functions defined on a semi-infinite interval but the nodes are equally spaced. It is shown that, under certain conditions, the interpolation process has poor approximation properties.

scholarly journals Strong result for real zeros of random algebraic polynomials

2001 ◽  
Vol 14 (4) ◽  
pp. 351-359 ◽  
Author(s):  
T. Uno
Keyword(s):  
Lower Bound ◽  
Random Variables ◽  
Strong Result ◽  
Algebraic Polynomials ◽  
Exceptional Set ◽  
Gaussian Random Variables ◽  
Real Zeros ◽  
Random Algebraic Polynomials

An estimate is given for the lower bound of real zeros of random algebraic polynomials whose coefficients are non-identically distributed dependent Gaussian random variables. Moreover, our estimated measure of the exceptional set, which is independent of the degree of the polynomials, tends to zero as the degree of the polynomial tends to infinity.

The least distance between extremums and minimal period of solutions to autonomous vector differential equations

2019 ◽  
Vol 485 (2) ◽  
pp. 142-144
Author(s):  
A. A. Zevin
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Lipschitz Constant ◽  
Minimal Period ◽  
Arbitrary Vector ◽  
Vector Norm ◽  
Sharp Lower Bound

Solutions x(t) of the Lipschitz equation x = f(x) with an arbitrary vector norm are considered. It is proved that the sharp lower bound for the distances between successive extremums of xk(t) equals π/L where L is the Lipschitz constant. For non-constant periodic solutions, the lower bound for the periods is 2π/L. These estimates are achieved for norms that are invariant with respect to permutation of the indices.

A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

10.37236/1188 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers

For $k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$ and on the k-color Ramsey numbers of $K_3$.

On the Crossing Number of $K_{m,n}$

10.37236/1748 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Nagi H. Nahas
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Crossing Number

The best lower bound known on the crossing number of the complete bipartite graph is : $$cr(K_{m,n}) \geq (1/5)(m)(m-1)\lfloor n/2 \rfloor \lfloor(n-1)/2\rfloor$$ In this paper we prove that: $$cr(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2 \rfloor \lfloor (n-1)/2 \rfloor + 9.9 \times 10^{-6} m^2n^2$$ for sufficiently large $m$ and $n$.

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