Exercises: 1. Consider the Lagrange coefficient polynomial L2k(x) that are used for quadratic interpolation at the nodes x,X1, and x2. Define g(x)=L2,0(x)+L2,1(x)+L22(x)-1. a. Show that g is a...

Exercises:<br>1. Consider the Lagrange coefficient polynomial L2k(x) that are used for quadratic<br>interpolation at the nodes x,X1, and x2. Define g(x)=L2,0(x)+L2,1(x)+L22(x)-1.<br>a. Show that g is a polynomial of degree <2.<br>b. Show that g(Xr)=0 for k=0,1,2.<br>

Extracted text: Exercises: 1. Consider the Lagrange coefficient polynomial L2k(x) that are used for quadratic interpolation at the nodes x,X1, and x2. Define g(x)=L2,0(x)+L2,1(x)+L22(x)-1. a. Show that g is a polynomial of degree <2. b.="" show="" that="" g(xr)="0" for="" k="">

Jun 03, 2022

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Exercises: 1. Consider the Lagrange coefficient polynomial L2k(x) that are used for quadratic interpolation at the nodes x,X1, and x2. Define g(x)=L2,0(x)+L2,1(x)+L22(x)-1. a. Show that g is a...

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