Q4) Consider the Lagrange coefficient polynomial L2x(x) that are used for quadratic interpolation at the nodes xo,X1, and x2. Define g(x)=L2,0(x)+L21(x)+L22(x)-1. a. Show that g is a polynomial of degree < 2. b. Show that g(Xµ)=0 for k=0,1,2.

Q4) Consider the Lagrange coefficient polynomial L2x(x) that are used for quadratic interpolation at the nodes xo,X1, and x2. Define g(x)=L2,0(x)+L21(x)+L22(x)-1. a. Show that g is a polynomial of degree < 2. b. Show that g(Xµ)=0 for k=0,1,2.

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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Q4) Consider the Lagrange coefficient polynomial L2(x) that are used for quadratic
interpolation at the nodes xo,X1, and x2. Define g(x)=L20(x)+L21(x)+L2.2(x)-1.
a. Show that g is a polynomial of degree < 2.
b. Show that g(x)=D0 for k=0,1,2.

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