Using Fixed-Point Iteration with an initial value of zero, find a root of the function: f (x) = x + 4x³ + 16x – 16 Stop iteration when the approximate error is less than 1%. Round-off intermediate values to 6 decimal places, and the final answer to 4 decimal places Hint: First, equate the function to 0. Then, isolate the constant term. Next, factor "x" on the left side of the equation. Finally, isolate x by dividing the equation by the factor of "x" on the left side of the equation. So, the iterative formula will be xk+1 = constant/ (a certain expression with Xk ) For example: Xk+1 -9+5 O 0.8278 none of the choices O 0.8272 O 0.8284 O 0.8289

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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1
Using Fixed-Point Iteration with an initial value of zero, find a root of the function:
f (x) = x4 + 4x³ + 16x – 16
Stop iteration when the approximate error is less than 1%.
Round-off intermediate values to 6 decimal places, and the final answer to 4 decimal places
Hint: First, equate the function to 0.
Then, isolate the constant term. Next, factor "x" on the left side of the equation.
Finally, isolate x by dividing the equation by the factor of "x" on the left side of the equation.
So, the iterative formula will be xk+1 = constant / (a certain expression with xk )
For example: Xk+1
-9+5
1.
O 0.8278
none of the choices
O 0.8272
O 0.8284
O 0.8289
Transcribed Image Text:Using Fixed-Point Iteration with an initial value of zero, find a root of the function: f (x) = x4 + 4x³ + 16x – 16 Stop iteration when the approximate error is less than 1%. Round-off intermediate values to 6 decimal places, and the final answer to 4 decimal places Hint: First, equate the function to 0. Then, isolate the constant term. Next, factor "x" on the left side of the equation. Finally, isolate x by dividing the equation by the factor of "x" on the left side of the equation. So, the iterative formula will be xk+1 = constant / (a certain expression with xk ) For example: Xk+1 -9+5 1. O 0.8278 none of the choices O 0.8272 O 0.8284 O 0.8289
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