a. Suppose P3(x) is the polynomial of degree 3 which interpolates f(x) = cos(3x) at xo = -1.5h, x1 = -0.5h, x2 = 0.5h, x3 = 1.5h. Find a reasonable upper bound on the error for co < x < x3. You can be "lazy," that is, bound |x – x;| for each i by |æ3 - xol- %3D %3D |34 car(3E)(34)"| 24 273.375 h9 24 b. [Extra credit] Same question, but now, DON'T be lazy, get the best possible bound on |q(x)| = |(x – x0)(x – 21)(x – x2)(x – x3)|. gla) = (x+ €)(x +€)-4)(x-24) = (x² 4*)( x²4) 96? = 2x g lo) = 4 2(fa) =-A* 76 fd-P,/ * = 4 %3D 3,378h4 W.
a. Suppose P3(x) is the polynomial of degree 3 which interpolates f(x) = cos(3x) at xo = -1.5h, x1 = -0.5h, x2 = 0.5h, x3 = 1.5h. Find a reasonable upper bound on the error for co < x < x3. You can be "lazy," that is, bound |x – x;| for each i by |æ3 - xol- %3D %3D |34 car(3E)(34)"| 24 273.375 h9 24 b. [Extra credit] Same question, but now, DON'T be lazy, get the best possible bound on |q(x)| = |(x – x0)(x – 21)(x – x2)(x – x3)|. gla) = (x+ €)(x +€)-4)(x-24) = (x² 4*)( x²4) 96? = 2x g lo) = 4 2(fa) =-A* 76 fd-P,/ * = 4 %3D 3,378h4 W.
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
Answer is given BUT need full detailed steps and process since I don't understand the concept.
![a. Suppose P3(x) is the polynomial of degree 3 which interpolates
f (x) = cos(3x) at xo = -1.5h, x1 = -0.5h, x2 = 0.5h, x3 = 1.5h.
Find a reasonable upper bound on the error for xo < x < x3. You
can be "lazy," that is, bound |x – x;| for each i by |x3 - xol.
1.
%3D
24
< 3° 64€273.375 h9
24
b. [Extra credit] Same question, but now, DON'T be lazy, get the
best possible bound on |q(x)| = |(x – xo)(x - ¤1)(x – ¤2) (x – c3)|.
gla) = (x+ )(x +€)&4)(x-24) = (x² 4*)( x²- 4)
= 2x [Zx²-
g (0) = 14* 2(Ea) = -A*
962
or X=±h
76
3.
4
%3D
3,37864](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb460c0c-d029-4e90-a450-1d82490780a1%2F9518b7d6-193a-4ca1-b90b-f7e550d7a7c6%2Ffs7l1cz_processed.png&w=3840&q=75)
Transcribed Image Text:a. Suppose P3(x) is the polynomial of degree 3 which interpolates
f (x) = cos(3x) at xo = -1.5h, x1 = -0.5h, x2 = 0.5h, x3 = 1.5h.
Find a reasonable upper bound on the error for xo < x < x3. You
can be "lazy," that is, bound |x – x;| for each i by |x3 - xol.
1.
%3D
24
< 3° 64€273.375 h9
24
b. [Extra credit] Same question, but now, DON'T be lazy, get the
best possible bound on |q(x)| = |(x – xo)(x - ¤1)(x – ¤2) (x – c3)|.
gla) = (x+ )(x +€)&4)(x-24) = (x² 4*)( x²- 4)
= 2x [Zx²-
g (0) = 14* 2(Ea) = -A*
962
or X=±h
76
3.
4
%3D
3,37864
Expert Solution
Step 1
_1.jpg)
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
