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8. One wants to solve the equation x+lnx = 0, whose root is r~ 0.5, using one or more of the following iterative methods: {i} xk+1 = -lnxk {i} xk+1 = ek {iii} Xk+1 = (a) Which of the three methods can be used? (b) Which method should be used? (c) Give an even better iterative formula. k+e-k 2

8. One wants to solve the equation x+lnx = 0, whose root is r~ 0.5, using one or more of the following iterative methods: {i} xk+1 = -lnxk {i} xk+1 = ek {iii} Xk+1 = (a) Which of the three methods can be used? (b) Which method should be used? (c) Give an even better iterative formula. k+e-k 2

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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8. One wants to solve the equation x+lnx = 0, whose root is r~ 0.5, using one or more of the following iterative methods: {i} xk+1 = -lnxk {ii} xk+1 = ek {iii} Chtech Xk+1 = 2 (a) Which of the three methods can be used? (b) Which method should be used? (c) Give an even better iterative formula.
Transcribed Image Text:8. One wants to solve the equation x+lnx = 0, whose root is r~ 0.5, using one or more of the following iterative methods: {i} xk+1 = -lnxk {ii} xk+1 = ek {iii} Chtech Xk+1 = 2 (a) Which of the three methods can be used? (b) Which method should be used? (c) Give an even better iterative formula.
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