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5. Consider the problem of taking the zeros of the the polynomial P(x) = ³x² - 6x over (2, 4). Below is an algorithm that may be used to numerically determine a zero. ²-1²-6 A: In+1 = In - 3r²-2-6* (a) Consider zo = 7. Numerically determine the value on which the sequence converges to Write the first 5 approximations of the algorithm. (b) By numerical means, estimate the order a and asymptotic error constant A of the sequence. (c) Provide an analytic proof for your claims in (c).

5. Consider the problem of taking the zeros of the the polynomial P(x) = ³x² - 6x over (2, 4). Below is an algorithm that may be used to numerically determine a zero. ²-1²-6 A: In+1 = In - 3r²-2-6* (a) Consider zo = 7. Numerically determine the value on which the sequence converges to Write the first 5 approximations of the algorithm. (b) By numerical means, estimate the order a and asymptotic error constant A of the sequence. (c) Provide an analytic proof for your claims in (c).

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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5. Consider the problem of taking the zeros of the the polynomial P(x) = ³-²-6r over (2,4). Below is an algorithm that may be used to numerically determine a zero. ²-1²-6 A: In+1 = In - 3r²-2-6* (a) Consider zo = 7. Numerically determine the value on which the sequence converges to Write the first 5 approximations of the algorithm. (b) By numerical means, estimate the order a and asymptotic error constant A of the sequence. (c) Provide an analytic proof for your claims in (c).
Transcribed Image Text:5. Consider the problem of taking the zeros of the the polynomial P(x) = ³-²-6r over (2,4). Below is an algorithm that may be used to numerically determine a zero. ²-1²-6 A: In+1 = In - 3r²-2-6* (a) Consider zo = 7. Numerically determine the value on which the sequence converges to Write the first 5 approximations of the algorithm. (b) By numerical means, estimate the order a and asymptotic error constant A of the sequence. (c) Provide an analytic proof for your claims in (c).
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