System of Linear Equations (Iterative Methods) Iterative methods ave based on successive Improvement of initial quesses for the sclution ITERCTIVE METHUDI: JACOBI METHOD Step 1. Rewrite the system Step 2. Initialize a value for the unknowns of zeru. tep 3. Perform iterction until the values af the unknown don't diverage anymore. Example: 3xty-z=3 2×t4y tz=フ X-Y+4z= ey Solution: x = 3-y+Z 3 y= 7-2x-Z 4 4-xty Ist Iteration X, = 3-0+O 3 Y.= 7-210)- (0) =175 2,:4-0+O ご 4 2ND ITERAMON: うーy,+ 2,- 3-115 +1 >0.75 3 3 Y2:7-2x,2、:フー2()-1 そz: 4-X,ty、 4-1+1.15 4-1+1.75 =1.1875 %3D
System of Linear Equations (Iterative Methods) Iterative methods ave based on successive Improvement of initial quesses for the sclution ITERCTIVE METHUDI: JACOBI METHOD Step 1. Rewrite the system Step 2. Initialize a value for the unknowns of zeru. tep 3. Perform iterction until the values af the unknown don't diverage anymore. Example: 3xty-z=3 2×t4y tz=フ X-Y+4z= ey Solution: x = 3-y+Z 3 y= 7-2x-Z 4 4-xty Ist Iteration X, = 3-0+O 3 Y.= 7-210)- (0) =175 2,:4-0+O ご 4 2ND ITERAMON: うーy,+ 2,- 3-115 +1 >0.75 3 3 Y2:7-2x,2、:フー2()-1 そz: 4-X,ty、 4-1+1.15 4-1+1.75 =1.1875 %3D
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 33E
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Question
Answer the following using Jacobi Method. Show complete solutions.
3. 9x1 + 2x2 - 3x3 = 7
x1 + 12x2 - 9x3 = 2
4x1 -6x2 + 14x3 = 1
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