Bounding the Lebesgue function for Lagrange interpolation in a simplex
نویسندگان
چکیده
منابع مشابه
On the Lebesgue Function of Weighted Lagrange Interpolation. Ii
The aim of this paper is to continue our investigation of the Lebesgue function of weighted Lagrange interpolation by considering Erdős weights on R and weights on [ 1;1]. The main results give lower bounds for the Lebesgue function on large subsets of the relevant domains. 1991 Mathematics subject classification (Amer. Math. Soc.): 41A05, 41A10.
متن کاملOn the Lebesgue constant for Lagrange interpolation on equidistant nodes
Properties of the Lebesgue function for Lagrange interpolation on equidistant nodes are investigated. It is proved that the Lebesgue function can be formulated both in terms of a hypergeometric function 2F1 and Jacobi polynomials. Moreover an integral expression of the Lebesgue function is also obtained. Finally, the asymptotic behavior of the Lebesgue constant is studied.
متن کاملLagrange Interpolation on a Lattice: Bounding Derivatives by Divided Differences
Fix an integer n > 0. For a multivariate function defined on a (not necessarily rectangular) lattice, an extension is constructed to have, ∀k ≤ n, derivatives of total degree k that are bounded by the function’s tensor product divided differences of total degree k times a constant independent of the lattice and the function. The extension is locally constructed, can have any prescribed smoothne...
متن کاملOn the Role of the Lebesgue Functions in the Theory of the Lagrange Interpolation'
where for n 1, 2 . . . . we have (1 .2) 1 fix,,,>xz„> . . .>x,,,, Then, as it is well known, for given values y,,,, there is exactly one polynomial g(x) of degree ~ aI such that g(x, •„)(r'1, 2, . . ., n) . If the values y, ., . are the values f(x,,,,) of a function f(x) defined in [-1, 1], then we call the corresponding g(x) polynomial "the nr'l interpolatory polynomial of f(x) belonging to A"...
متن کاملOn the Integral of the Lebesgue Function of Interpolation
;.Ja, b) = max Z A(x)1 if -I -a < b -1 . a~xs6 k=1 The quantity 1) called Lebesgue constant plays an important role in the theory of Lagrange interpolation ; as G . FABER [1] showed 1 (2) ~ n (l, 1) -c 1 log n for an arbitrary system of nodes (1). Moreover, S . BERNSTEIN [2] proved that (3) Acta Mathematica Academiae Scientiarum Hungaricae Tomus 32 (1-2), (1978), 191-195. ON THE INTEGRAL OF THE...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1983
ISSN: 0021-9045
DOI: 10.1016/0021-9045(83)90140-5