Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
7. Apply the Gauss-Seidel method to Exercise 3.

7. Apply the Gauss-Seidel method to Exercise 3.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
Question
Please answer nunber 7
Gauss-Seidel Method: Example 2 Rewriting each equation With an initial guess of [12 3 -5 a, 15 189 3 a2 =28 1-0 3 76 X₁ x₂ = X₂ 7 13 a 1-3x₂ + 5x₂ 12 28-x₁ - 3x₂ 5 76-3x, -7x₂ 13 X₂ x₁ = 1-3(0)+5(1) 12 x₂ = 28-(0.5)-3(1) 5 = 4.9000 76-3(0.50000)-7(4.9000) 13 = 0.50000 = 3.0923
Transcribed Image Text:Gauss-Seidel Method: Example 2 Rewriting each equation With an initial guess of [12 3 -5 a, 15 189 3 a2 =28 1-0 3 76 X₁ x₂ = X₂ 7 13 a 1-3x₂ + 5x₂ 12 28-x₁ - 3x₂ 5 76-3x, -7x₂ 13 X₂ x₁ = 1-3(0)+5(1) 12 x₂ = 28-(0.5)-3(1) 5 = 4.9000 76-3(0.50000)-7(4.9000) 13 = 0.50000 = 3.0923
In Exercises 1-4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x₁, x2,...,x₁) = (0, 0, . . . , 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. 1. 3x₁ x₂ = 2 2. - 4x₁ + 2x₂ = -6 3x₁ - 5x₂ = 1 x₁ + 4x₂ = 5 3. 2x₁ - x₂ 2 4. 4x₁ + x₂ + x3 - x₁ = 3x₂ + x3 = -2 X1 - 7x₂ + 2x3 -x₁ + x₂-3x3 = -6 3x₁ 5. Apply the Gauss-Seidel method to Exercise 1. 6. Apply the Gauss-Seidel method to Exercise 2. 7. Apply the Gauss-Seidel method to Exercise 3. 8. Apply the Gauss-Seidel method to Exercise 4. || = = + 4x3 7 2 11
Transcribed Image Text:In Exercises 1-4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x₁, x2,...,x₁) = (0, 0, . . . , 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. 1. 3x₁ x₂ = 2 2. - 4x₁ + 2x₂ = -6 3x₁ - 5x₂ = 1 x₁ + 4x₂ = 5 3. 2x₁ - x₂ 2 4. 4x₁ + x₂ + x3 - x₁ = 3x₂ + x3 = -2 X1 - 7x₂ + 2x3 -x₁ + x₂-3x3 = -6 3x₁ 5. Apply the Gauss-Seidel method to Exercise 1. 6. Apply the Gauss-Seidel method to Exercise 2. 7. Apply the Gauss-Seidel method to Exercise 3. 8. Apply the Gauss-Seidel method to Exercise 4. || = = + 4x3 7 2 11
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS