Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
The 3x3 system below has solutions x₁ = 1, x₂ = -2 and X3=07 4x+2x₂-2x3 = 0 2x1-6x2 - 2x3 = 14 3X1-Xǝ+4x3 = 5 10 Explain why this system is not quickly strictly diagonally dominant (hereafter 5DD)

The 3x3 system below has solutions x₁ = 1, x₂ = -2 and X3=07 4x+2x₂-2x3 = 0 2x1-6x2 - 2x3 = 14 3X1-Xǝ+4x3 = 5 10 Explain why this system is not quickly strictly diagonally dominant (hereafter 5DD)

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
icon
Related questions
Question

ANSWER ONLY (i)

Round off to 3 decimal place The 3x3 system below has solutions x₁=1, x₂ = -2 and X₂=0 4x₁+2x₂=2x3 = 0 2x₁-6x2 - 2x3 = 14 3X₁-X₂ +4X3 = 5 (1) Explain why this system is not quickly strictly diagonally dominant (hereafter 5DD) (i) Using the initial approximation X₁0 = 0.75, X₁² = -1.75 and X300) = -0.35, apply three iterations of the Jacobi Method to the above system 208 .(0) (0) (iii) Taking the initial approximation X₂₁ =0.75, X₂ = -1.75 and x300) = -0.35, apply three iterations of the Jacobi Method to the above system (iv) Will the Jacobi and Gauss-Siedel iterates For all 3x3 linear systems that are not SDD always eliverge? If not, give an example of a system that is not SDD, but for which the Jacobi and Grauss- Siedel iterates converge to the solution of the system.
Transcribed Image Text:Round off to 3 decimal place The 3x3 system below has solutions x₁=1, x₂ = -2 and X₂=0 4x₁+2x₂=2x3 = 0 2x₁-6x2 - 2x3 = 14 3X₁-X₂ +4X3 = 5 (1) Explain why this system is not quickly strictly diagonally dominant (hereafter 5DD) (i) Using the initial approximation X₁0 = 0.75, X₁² = -1.75 and X300) = -0.35, apply three iterations of the Jacobi Method to the above system 208 .(0) (0) (iii) Taking the initial approximation X₂₁ =0.75, X₂ = -1.75 and x300) = -0.35, apply three iterations of the Jacobi Method to the above system (iv) Will the Jacobi and Gauss-Siedel iterates For all 3x3 linear systems that are not SDD always eliverge? If not, give an example of a system that is not SDD, but for which the Jacobi and Grauss- Siedel iterates converge to the solution of the system.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

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