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nswer the following using Jacobi Method. Show complete solutions. 1.) 15x + 2y - z = -200       2x + 12y + z = -250        x + 2y + 8z = 30

nswer the following using Jacobi Method. Show complete solutions. 1.) 15x + 2y - z = -200       2x + 12y + z = -250        x + 2y + 8z = 30

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
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Answer the following using Jacobi Method. Show complete solutions.

1.) 15x + 2y - z = -200
      2x + 12y + z = -250
       x + 2y + 8z = 30

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Step 3. Perform iterction until the values af System of Linear Equations (Iterative Methads) Iterative methads ave based on successive improvement of initial quesser for the sdlution ITERATIVE METHUDI : JACORI METHOD Step 1. Rewrite the system Step 2. Initialize a value for the unknouns of zeru. tep 3. Perform iterction until the values al the unknawn dan't divevge anymore. falut Example: A 3xty-Z =3 2×+4y+zニフ Solution: そtん-e = メ Y=7-2x-Z 4 Z:4-xty スキメーh : x:0; y=0,2=0 Ist Itercition X,こ3-0+O 3 Y.= 7-2(0) - (0? =1.75 Z,?4-04 O 4 2ND ITERAION: メ2ラーy,ナ21-3-175+l>0.75 3 3 Y2:1-2x,*2フー2-D.1 そz: 4-Xty、 4-1t15 4-1+1.75 =1.1875
Transcribed Image Text:Step 3. Perform iterction until the values af System of Linear Equations (Iterative Methads) Iterative methads ave based on successive improvement of initial quesser for the sdlution ITERATIVE METHUDI : JACORI METHOD Step 1. Rewrite the system Step 2. Initialize a value for the unknouns of zeru. tep 3. Perform iterction until the values al the unknawn dan't divevge anymore. falut Example: A 3xty-Z =3 2×+4y+zニフ Solution: そtん-e = メ Y=7-2x-Z 4 Z:4-xty スキメーh : x:0; y=0,2=0 Ist Itercition X,こ3-0+O 3 Y.= 7-2(0) - (0? =1.75 Z,?4-04 O 4 2ND ITERAION: メ2ラーy,ナ21-3-175+l>0.75 3 3 Y2:1-2x,*2フー2-D.1 そz: 4-Xty、 4-1t15 4-1+1.75 =1.1875
Sheuld oo be less than 0.005, 5 decimdl 3RD ITERATION: メッ=3- y2t2, %3D 3-1+1.1875 =1.0625 %3D Yo:フ-2x, -Z2 7-210.75)-1-1875 こ 1.078125 2,- 4-メetyz 4 - C0-75) +| %3D i,0625 4 'Iteration 1 1.75 2. 0-75 |-1875 3 1.0425 1.078125 U -994792 0.953125 1.003906 10625 4 1.016927 1-001628 0-989583 0-995985 0.994141 0.990175 0.09953 7 1-000676 1.00303 As required, the difference of the last iteaticn 1に2、1:んり1こメ |
Transcribed Image Text:Sheuld oo be less than 0.005, 5 decimdl 3RD ITERATION: メッ=3- y2t2, %3D 3-1+1.1875 =1.0625 %3D Yo:フ-2x, -Z2 7-210.75)-1-1875 こ 1.078125 2,- 4-メetyz 4 - C0-75) +| %3D i,0625 4 'Iteration 1 1.75 2. 0-75 |-1875 3 1.0425 1.078125 U -994792 0.953125 1.003906 10625 4 1.016927 1-001628 0-989583 0-995985 0.994141 0.990175 0.09953 7 1-000676 1.00303 As required, the difference of the last iteaticn 1に2、1:んり1こメ |
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