Adaptive rejection Metropolis sampling using Lagrange interpolation polynomials of degree 2

2008 ◽  
Vol 52 (7) ◽  
pp. 3408-3423 ◽  
Author(s):  
Renate Meyer ◽  
Bo Cai ◽  
François Perron
Keyword(s):  
Lagrange Interpolation ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials ◽  
Adaptive Rejection Metropolis Sampling

scholarly journals On Lagrange interpolation with equally spaced nodes

2000 ◽  
Vol 62 (3) ◽  
pp. 357-368 ◽  
Author(s):  
Michael Revers
Keyword(s):  
Rate Of Convergence ◽  
Lagrange Interpolation ◽  
End Points ◽  
Quantitative Version ◽  
Equidistant Nodes ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials ◽  
Exact Rate Of Convergence

A well-known result due to S.N. Bernstein is that sequence of Lagrange interpolation polynomials for |x| at equally spaced nodes in [−1, 1] diverges everywhere, except at zero and the end-points. In this paper we present a quantitative version concerning the divergence behaviour of the Lagrange interpolants for |x|3 at equidistant nodes. Furthermore, we present the exact rate of convergence for the interpolatory parabolas at the point zero.

scholarly journals Some integer-valued trigonometric sums

1997 ◽  
Vol 40 (2) ◽  
pp. 393-401 ◽  
Author(s):  
Graeme J. Byrne ◽  
Simon J. Smith
Keyword(s):  
Chebyshev Polynomial ◽  
Lagrange Interpolation ◽  
Recurrence Relations ◽  
Trigonometric Sums ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials

It is shown that for m = 1,2,3,…, the trigonometric sums and can be represented as integer-valued polynomials in n of degrees 2m – 1 and 2m, respectively. Properties of these polynomials are discussed, and recurrence relations for the coefficients are obtained. The proofs of the results depend on the representations of particular polynomials of degree n – 1 or less as their own Lagrange interpolation polynomials based on the zeros of the nth Chebyshev polynomial Tn(x) = cos(narccos x), -1≤x≤1.

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