Solve the nonlinear system using Newton's method with the given initial vector. Terminate the process when the maximum norm of the difference between successive iterates is less than 5 x 10-6. f(x, y, z) 1. g(x, y, z) h(x, y, z) = = = 2 x² + y² + z² - 1 x² + z² -0.25 x² + y² - 4z 0 = 0 = 0 = x(0) = [1_1_1]T.
Solve the nonlinear system using Newton's method with the given initial vector. Terminate the process when the maximum norm of the difference between successive iterates is less than 5 x 10-6. f(x, y, z) 1. g(x, y, z) h(x, y, z) = = = 2 x² + y² + z² - 1 x² + z² -0.25 x² + y² - 4z 0 = 0 = 0 = x(0) = [1_1_1]T.
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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![Solve the nonlinear system using Newton's method with the given initial vector. Terminate
the process when the maximum norm of the difference between successive iterates is less
than 5 × 10-6.
f(x, y, z) = x² + y² + 2²-1
1. g(x, y, z)
x² + z² -0.25
h(x, y, z)
x² + y² - 4z
=
-
= 0
0
0
=
=
X(0)
=
= [1_1_1]ª.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa84a4758-fcfb-469c-8938-cd0c632fc193%2F483820c2-9f74-41f2-926b-6e98bec48129%2F77v5fc_processed.png&w=3840&q=75)
Transcribed Image Text:Solve the nonlinear system using Newton's method with the given initial vector. Terminate
the process when the maximum norm of the difference between successive iterates is less
than 5 × 10-6.
f(x, y, z) = x² + y² + 2²-1
1. g(x, y, z)
x² + z² -0.25
h(x, y, z)
x² + y² - 4z
=
-
= 0
0
0
=
=
X(0)
=
= [1_1_1]ª.
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