This book gives a systematic survey on the most significant results of interpolation theory in
the last forty years. It deals with Lagrange interpolation including lower estimates, fine and …

For a wide classof weights, a systematic investigation of the convergence-divergence
behavior of Lagrange interpolation is initiated. A system of nodes with optimal Lebesgue …

In this brief survey special attention is paid to some recent procedures for constructing
optimal interpolation processes, ie, with Lebesgue constant having logarithmic behaviour. A …

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Properties of the Lebesgue function associated with interpolation at the Chebyshev nodes
{\cos(2k-1)π(2n),\,k=1,2,⋯,n\} are studied. It is proved that the relative maxima of the …

Lagrange interpolation is a classical method for approximating a continuous function by a
polynomial that agrees with the function at a number of chosen points (the “nodes”) …

In 1931, S. Bernstein [l] conjectured that 1~ P,/I is minimal when fl, equioscillates, ie, when
h,(t)= &,(t)=...= X,(t). Later, Erdijs [7] added to this the conjecture that there is exactly one …

This reference book provides the main definitions, theorems and techniques in the theory of
Birkhoff interpolation by polynomials. The book begins with an article by GG Lorentz that …

This paper is concerned with the approximate evaluation of -1^1k(x)f(x)d_x, where k is
Lebesgue integrable and f is at least Riemann integrable, and preferably smooth. The …

Given any data points ${x_1},\ldots,{x_n} $ in ${{\mathbf {R}}^ s} $ and values $ S_p^ q $ of a
function f, Shepard's global interpolation formula reads as follows:\[S_p^ 0f (x)=\sum\limits _i …