Exercises:1. Consider the Lagrange coefficient polynomial L2.a(x) that are used for quadraticinterpolation 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(xx)%3D0 for k=0,1,2.2. Consider the function f(x)=sin(x) on the interval [0,1]. Use theorem(3.3) to determine thestep size h so that:a. linear Lagrange interpolation has an accuracy of 10°.b. quadratic Lagrange interpolation has an accuracy of 10°.c. cubic Lagrange interpolation has an accuracy of 10".

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1. Consider the Lagrange coefficient polynomial L2.x(x) that are used for quadratic interpolation at the nodes x0,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(x)=0 for k=0,1,2.

1. Consider the Lagrange coefficient polynomial L2.x(x) that are used for quadratic interpolation at the nodes x0,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(x)=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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