3. Consider the following data set -2012 f(x₂) 5 1 -1 5 (a) Construct the quadratic Lagrange interpolating polynomial P2(x) that interpo- lates f(x) at x; for i = 0, 1, 2. Sketch the three Lagrange basis polynomials on [To, x2]. (b) Construct the cubic Lagrange interpolating polynomial P3(r) that interpolates f(x) at x; for i = 0, 1, 2, 3. Sketch the four Lagrange basis polynomials on [ro, x3].
3. Consider the following data set -2012 f(x₂) 5 1 -1 5 (a) Construct the quadratic Lagrange interpolating polynomial P2(x) that interpo- lates f(x) at x; for i = 0, 1, 2. Sketch the three Lagrange basis polynomials on [To, x2]. (b) Construct the cubic Lagrange interpolating polynomial P3(r) that interpolates f(x) at x; for i = 0, 1, 2, 3. Sketch the four Lagrange basis polynomials on [ro, x3].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Second photo is what to complete in D, in the first photo
please do all 4 if not. Try to complete the last part
Transcribed Image Text:3. Consider the same data set as that in Problem 3 of Homework 1.
-2 0 1 2
Xi
f(x₁) 5 1 -1 5
(a) Construct the divided difference table for points zi, i = 0,
the matlab file divdif.m on Canvas to check your answer.
,3. You may use
(b) Construct the Newton forward divided difference interpolating polynomials Q1 (1)
(using ri, i = 0, 1), Q2(r) (using zi, i = 0, 1, 2), and Q3(r) (using zi, i = 0, 1, 2, 3).
(c) Construct the Newton backward divided difference interpolating polynomial
R3(x) using ri, i = 0, 1, 2, 3.
(d) P3(x) in problem 3 of Homework 1, Q3(r) and R3(z) interpolate the same data
set. Verify the uniqueness of interpolating polynomial by showing that Q3 (2) and
R3(x) are the same. (Of course they are also the same as P3 (2) from Problem 3
of Homework 1.)
(6)
![3. Consider the following data set
Xi -2 0 1 2
f(xi) 5 1 -1 5
(a) Construct the quadratic Lagrange interpolating polynomial P₂(x) that interpo-
lates f(x) at x, for i = 0, 1, 2. Sketch the three Lagrange basis polynomials on
[x0, x2].
(b) Construct the cubic Lagrange interpolating polynomial P3(x) that interpolates
f(x) at x, for i = 0, 1, 2, 3. Sketch the four Lagrange basis polynomials on [xo, x3].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c842333-6f00-4a4b-9f61-7bda344711a4%2F45da49b3-8891-44b9-80df-20f03a18a768%2Fv0q4rkr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Consider the following data set
Xi -2 0 1 2
f(xi) 5 1 -1 5
(a) Construct the quadratic Lagrange interpolating polynomial P₂(x) that interpo-
lates f(x) at x, for i = 0, 1, 2. Sketch the three Lagrange basis polynomials on
[x0, x2].
(b) Construct the cubic Lagrange interpolating polynomial P3(x) that interpolates
f(x) at x, for i = 0, 1, 2, 3. Sketch the four Lagrange basis polynomials on [xo, x3].
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Step 1: Introduction
VIEWStep 2: Calculating the divided differences
VIEWStep 3: Calculating the Newton Forward divided difference interpolating polynomial
VIEWStep 4: Calculating the Newton backward divided difference interpolating polynomial
VIEWStep 5: Constructing the quadratic Lagrange interpolating polynomial
VIEWStep 6: sketching the basis polynomials
VIEWStep 7: Constructing the cubic Lagrange interpolating polynomial
VIEWStep 8: sketching the basis polynomials
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