(b) To find the daily optimum production number of Portland cement in a factory, one needs to solve the following equations based on the ingredient of cement. The unknowns are lime, x1; silica, x2; alumina, x3; and iron oxide, X4. 10x₁x₂ + 2x3 = 6 - -X₁ + 11x₂x3 + 3x4 = 25 2x₁ - x₂ + 10x3 - X4 = -11 3x₂x3 + 8x4 = 15 Use the Gauss-Seidel iterative technique to find approximate solutions to X₁, X2, X3, and x4. Starting with x = (0, 0, 0, 0) and iterating until max{|x (k+1)-x(k)|} <ε = 0.0005
(b) To find the daily optimum production number of Portland cement in a factory, one needs to solve the following equations based on the ingredient of cement. The unknowns are lime, x1; silica, x2; alumina, x3; and iron oxide, X4. 10x₁x₂ + 2x3 = 6 - -X₁ + 11x₂x3 + 3x4 = 25 2x₁ - x₂ + 10x3 - X4 = -11 3x₂x3 + 8x4 = 15 Use the Gauss-Seidel iterative technique to find approximate solutions to X₁, X2, X3, and x4. Starting with x = (0, 0, 0, 0) and iterating until max{|x (k+1)-x(k)|} <ε = 0.0005
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
![(b)
To find the daily optimum production number of Portland cement in a
factory, one needs to solve the following equations based on the ingredient
of cement. The unknowns are lime, x1; silica, x2; alumina, x3; and iron oxide,
X4.
10x1 – x2 + 2x3 = 6
-X1 + 11x2 – x3 + 3x4 = 25
2x1 - x2 + 10x3 – X4 = -11
3x2 - x3 +8x4 = 15
Use the Gauss-Seidel iterative technique to find approximate solutions to XỊ,
X2, X3, and x4. Starting with x (0, 0, 0, 0)" and iterating until
max{]x(*+1) – x(k)} < e = 0.0005](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6b8c48d-17cf-4493-a908-562b64c019d9%2F18431fd8-f63b-4490-9de6-737137098892%2F1o4orsq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b)
To find the daily optimum production number of Portland cement in a
factory, one needs to solve the following equations based on the ingredient
of cement. The unknowns are lime, x1; silica, x2; alumina, x3; and iron oxide,
X4.
10x1 – x2 + 2x3 = 6
-X1 + 11x2 – x3 + 3x4 = 25
2x1 - x2 + 10x3 – X4 = -11
3x2 - x3 +8x4 = 15
Use the Gauss-Seidel iterative technique to find approximate solutions to XỊ,
X2, X3, and x4. Starting with x (0, 0, 0, 0)" and iterating until
max{]x(*+1) – x(k)} < e = 0.0005
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