On the convergence of the derivatives of Lagrange interpolating polynomials

1990 ◽  
Vol 55 (3-4) ◽  
pp. 323-325 ◽  
Author(s):  
K. Balázs
Keyword(s):  
Interpolating Polynomials ◽  
Derivatives Of ◽  
Lagrange Interpolating Polynomials

On the derivatives of Hermite-Fejér interpolating polynomials

1990 ◽  
Vol 55 (3-4) ◽  
pp. 301-309
Author(s):  
J. Szabados ◽  
A. K. Varma
Keyword(s):  
Interpolating Polynomials ◽  
Derivatives Of

scholarly journals On approximation by trigonometric Lagrange interpolating polynomials

1989 ◽  
Vol 40 (3) ◽  
pp. 425-428 ◽  
Author(s):  
T.F. Xie ◽  
S.P. Zhou
Keyword(s):  
Upper Bound ◽  
Best Approximation ◽  
Arbitrary Degree ◽  
Interpolating Polynomials ◽  
Lagrange Interpolating Polynomials

It is well-known that the approximation to f(x) ∈ C2π, by nth trigonometric Lagrange interpolating polynomials with equally spaced nodes in C2π, has an upper bound In(n)En(f), where En(f) is the nth best approximation of f(x). For various natural reasons, one can ask what might happen in Lp space? The present paper indicates that the result about the trigonometric Lagrange interoplating approximation in Lp space for 1 < p < ∞ may be “bad” to an arbitrary degree.

On approximation by trigonometric Lagrange interpolating polynomials II

1992 ◽  
Vol 45 (2) ◽  
pp. 215-221 ◽  
Author(s):  
P.B. Borwein ◽  
T.F. Xie ◽  
S.P. Zhou
Keyword(s):  
Interpolating Polynomials ◽  
Lagrange Interpolating Polynomials

We show that trigonometric Lagrange interpolating approximation with arbitrary real distinct nodes in Lp space for 1 ≤ p < ∞, as that with equally spaced nodes in Lp space for 1 < p < ∞ in an earlier paper by T.F. Xie and S.P. Zhou, may also be arbitrarily “bad”. This paper is a continuation of this earlier work by Xie and Zhou, but uses a different method.

Some Properties of a Certain set of Interpolating Polynomials

1975 ◽  
Vol 18 (4) ◽  
pp. 529-537 ◽  
Author(s):  
David J. Leeming
Keyword(s):  
Interpolating Polynomials ◽  
Even Order ◽  
Derivatives Of

A Lidstone series provides a (formal) two-point expansion of a given functionf(x)in terms of its derivatives of even order at the nodes 0 and 1 and takes the form.

scholarly journals Solution of Nonlinear Volterra-Fredholm Integrodifferential Equations via Hybrid of Block-Pulse Functions and Lagrange Interpolating Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hamid Reza Marzban ◽  
Sayyed Mohammad Hoseini
Keyword(s):  
Differential Equations ◽  
Hybrid Method ◽  
High Order ◽  
Integrodifferential Equations ◽  
Algebraic Equations ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Interpolating Polynomials ◽  
Lagrange Interpolating Polynomials

An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations to the solution of algebraic equations whose solution is much more easier than the original one. The validity and applicability of the proposed method are demonstrated through illustrative examples. The method is simple, easy to implement and yields very accurate results.

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