1. Use Eq. (3.10) or Algorithm 3.2 to construct interpolating polynomials of degree one, two, and three for the following data. Approximate the specified value using each of the polynomials. f(8.4) if ƒ (8.1) = 16.94410, ƒ (8.3) = 17.56492, f(8.6) = 18.50515, ƒ (8.7) = 18.82091 b. f (0.9) if f (0.6) а. %3D -0.17694460, ƒ (0.7) = 0.01375227, f(0.8) 0.22363362, ƒ (1.0) 0.65809197
1. Use Eq. (3.10) or Algorithm 3.2 to construct interpolating polynomials of degree one, two, and three for the following data. Approximate the specified value using each of the polynomials. f(8.4) if ƒ (8.1) = 16.94410, ƒ (8.3) = 17.56492, f(8.6) = 18.50515, ƒ (8.7) = 18.82091 b. f (0.9) if f (0.6) а. %3D -0.17694460, ƒ (0.7) = 0.01375227, f(0.8) 0.22363362, ƒ (1.0) 0.65809197
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
Related questions
Question
plz solve q1 part a equation 3.10 and algorathim is attached u can use any of them
![126
CHAPTER 3 - Interpolation and Polynomiel Approximation
As might be expected from the evaluation of a and a1, the required constants are
= flx0,X1,2....),
for each k = 0,1,...,n. So P,(x) can be rewritten in a form called Newton's Divided-
Difference:
P(x) = fl%a]+£ S%o1.....(x- a) ... (x - 4-1).
(3. 10)
The value of f(xo, a...] isindependent of the arder of the numbers x0,X1..... , as
shown in Exercise 21.
The generation of the divided differences is out lined in Table 3.9. Two fouth and one
fifth difference can akso be determined from these data.
Table 3.9
Fist
Secoal
diided difkerenes
Third
divided diflecnces
dividel difkerenes
-
flal- fll
flal- flal
flal
flul- fal
fl.al- fla.al
Newton's Divided-Difference Formula
ALGORITHIM
3.2
Toobtain the divided-difference coefficients of the interpolatory polynomial Pan the (n+ 1)
distinct mumbers Xg, Xp. ..., for the function f:
INPUT numbers Ag, X1. ...; values f(x). f (x),.... f(4) as Fan. F1,0 --. Fao
OUTPUT the numbers Fao. F1.t ...Fan where
P,(x) = Fop +EFJI«- x). (Fu is f[xg, X1. ....1.)
Step 1 For i- 1, 2,...,"
For j=1,2...i
Fu-- F-y- (Fu - fl..-)
set Fy =
Step 2 OUTPUT (Fan.Fu.....Fa):
STOP.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b35480d-69c8-4574-97fb-0771b96e271d%2F060c297b-eac7-4422-b486-c5039c168fad%2F8wacewp_processed.png&w=3840&q=75)
Transcribed Image Text:126
CHAPTER 3 - Interpolation and Polynomiel Approximation
As might be expected from the evaluation of a and a1, the required constants are
= flx0,X1,2....),
for each k = 0,1,...,n. So P,(x) can be rewritten in a form called Newton's Divided-
Difference:
P(x) = fl%a]+£ S%o1.....(x- a) ... (x - 4-1).
(3. 10)
The value of f(xo, a...] isindependent of the arder of the numbers x0,X1..... , as
shown in Exercise 21.
The generation of the divided differences is out lined in Table 3.9. Two fouth and one
fifth difference can akso be determined from these data.
Table 3.9
Fist
Secoal
diided difkerenes
Third
divided diflecnces
dividel difkerenes
-
flal- fll
flal- flal
flal
flul- fal
fl.al- fla.al
Newton's Divided-Difference Formula
ALGORITHIM
3.2
Toobtain the divided-difference coefficients of the interpolatory polynomial Pan the (n+ 1)
distinct mumbers Xg, Xp. ..., for the function f:
INPUT numbers Ag, X1. ...; values f(x). f (x),.... f(4) as Fan. F1,0 --. Fao
OUTPUT the numbers Fao. F1.t ...Fan where
P,(x) = Fop +EFJI«- x). (Fu is f[xg, X1. ....1.)
Step 1 For i- 1, 2,...,"
For j=1,2...i
Fu-- F-y- (Fu - fl..-)
set Fy =
Step 2 OUTPUT (Fan.Fu.....Fa):
STOP.
Transcribed Image Text:1. Use Eq. (3.10) or Algorithm 3.2 to construct interpolating polynomials of degree one, two, and three
for the following data. Approximate the specified value using each of the polynomials.
f(8.4) if ƒ (8.1) = 16.94410, f (8.3) = 17.56492, ƒ(8.6) = 18.50515, ƒ (8.7) = 18.82091
f (0.9) if f(0.6)
а.
b.
-0.17694460, f (0.7) = 0.01375227, f(0.8) = 0.22363362, ƒ (1.0)
0.65809197
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