5. Show that for any set of interpolant nodes, we haveE"6 (x) = x™j=0for all m e {0,1,...,n}, where l;(x) is the jth Lagrange polynomial.

Consider ,any set of k + 1 data points

Answered: Show that for any set of interpolant…

Show that for any set of interpolant nodes, we have j=0 for all m € {0, 1, ., n}, where l,(r) is the jth Lagrange polynomial.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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5. Show that for any set of interpolant nodes, we have
E"6 (x) = x™
j=0
for all m e {0,1,...,n}, where l;(x) is the jth Lagrange polynomial.

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