Exercise: Newton's Divided Difference Method (a) Construct a divided difference table from the following data: 0.6 0.9 3.3201 6.0496 0.3 f(x) 1.8221 (b) Use the table presented in Question (a) along with Newton's Divided Difference Formula to approximate f(0.1) with a polynomial of degree three. Start with x = 0. Estimate the error in the approximation. 1 1.2 11.0232 (c) Use the table presented in Question (a) along with Newton's Divided Difference Formula to approximate f (1.1) with a polynomial of degree three. Start with x4 = 1.2. Estimate the error in the approximation. (Hint: Read the divided difference table from the "downside up".)
Exercise: Newton's Divided Difference Method (a) Construct a divided difference table from the following data: 0.6 0.9 3.3201 6.0496 0.3 f(x) 1.8221 (b) Use the table presented in Question (a) along with Newton's Divided Difference Formula to approximate f(0.1) with a polynomial of degree three. Start with x = 0. Estimate the error in the approximation. 1 1.2 11.0232 (c) Use the table presented in Question (a) along with Newton's Divided Difference Formula to approximate f (1.1) with a polynomial of degree three. Start with x4 = 1.2. Estimate the error in the approximation. (Hint: Read the divided difference table from the "downside up".)
Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Exercise: Newton's Divided Difference Method
(a) Construct a divided difference table from the following data:
0
0.3
0.6
1.8221
3.3201
0.9
6.0496
1.2
11.0232
f(x)
(b) Use the table presented in Question (a) along with Newton's Divided Difference Formula to
approximate f (0.1) with a polynomial of degree three. Start with x = 0.
Estimate the error in the approximation.
(c) Use the table presented in Question (a) along with Newton's Divided Difference Formula to
approximate f(1.1) with a polynomial of degree three. Start with x4 = 1.2.
Estimate the error in the approximation. (Hint: Read the divided difference table from the
"downside up".)
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