Q4) Consider the following function f(x) = x³ + 6x² - 4x - 2 a) Find all fixed-point formulations of the above function. b) Apply the condition of convergence to each of the above formulation to determine the convergence of each formulation when xo = 1? State the condition of convergence for Fixed-Point method. c) The following table provides iteration of Fixed-Point method using suitable fixed- point formulation in part a and b that rapidly convergence. i. Compute x₁. ii. Compute the percentage relative approximate error. €a (%) i 0 1 2 3 4 5 xi 1
Q4) Consider the following function f(x) = x³ + 6x² - 4x - 2 a) Find all fixed-point formulations of the above function. b) Apply the condition of convergence to each of the above formulation to determine the convergence of each formulation when xo = 1? State the condition of convergence for Fixed-Point method. c) The following table provides iteration of Fixed-Point method using suitable fixed- point formulation in part a and b that rapidly convergence. i. Compute x₁. ii. Compute the percentage relative approximate error. €a (%) i 0 1 2 3 4 5 xi 1
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

Transcribed Image Text:Q4) Consider the following function
f(x) = x³ + 6x² - 4x - 2
a) Find all fixed-point formulations of the above function.
b) Apply the condition of convergence to each of the above formulation to determine the
convergence of each formulation when xo = 1? State the condition of convergence for
Fixed-Point method.
c) The following table provides iteration of Fixed-Point method using suitable fixed-
point formulation in part a and b that rapidly convergence.
i.
Compute x₁.
ii.
Compute the percentage relative approximate error.
€a (%)
i
0
1
2
3
4
5
Xi
1
Expert Solution

Step 1
Step by step
Solved in 4 steps with 4 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,

