Now let us experiment with the sequence {ek}keN C R+ given by ek+1 = aek, k = 0, 1, 2, ... (*) for fixed constants a > 0 and p > 0, which models the errors of a numerical method with order of convergence p. d) Apply the logarithm to both sides of the recursion (*). Use the rules for logarithms to deduce that all pairs (log(ek), log(ek+1)) are located on a straight line in R2. What does the slope of this line tell us?
Now let us experiment with the sequence {ek}keN C R+ given by ek+1 = aek, k = 0, 1, 2, ... (*) for fixed constants a > 0 and p > 0, which models the errors of a numerical method with order of convergence p. d) Apply the logarithm to both sides of the recursion (*). Use the rules for logarithms to deduce that all pairs (log(ek), log(ek+1)) are located on a straight line in R2. What does the slope of this line tell us?
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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Transcribed Image Text:Now let us experiment with the sequence {ek}kEN C R+ given by
ek+1=aek, k = 0, 1, 2, ...
for fixed constants a > 0 and p > 0, which models the errors of a numerical
method with order of convergence p.
d) Apply the logarithm to both sides of the recursion (*). Use the rules
for logarithms to deduce that all pairs (log(ek), log(ek+1)) are located
on a straight line in R². What does the slope of this line tell us?
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